Ecological Outcomes of Tortoise Restoration on Santa Fe Island

     

Summary: This document provides a synthesis of initial demographic outcomes of the release of 551 captively bred Española tortoises on the island of Santa Fe in the Galapagos archipelago. I summarize the results from three separate analyses on the (1) growth, (2) survival, and (3) dispersal of these tortoises from 2015 to 2020.

A juvenile Española tortoise on Santa Fe Island.

I’ll also examine potential impacts of tortoises on the Santa Fe land iguana population, the only major (extant) native herbivore on Santa Fe, as well as the endemic cactus population.

Growth

---

Tortoise morphology—Santa Fe

First I’ll load the tortoise data with body metrics and time intervals.

library(readxl)
# load recapture data
sf_recaps <- suppressMessages(read_excel(
  path = "data/tortoise_data_Mar_2020.xlsx",
  sheet = "Marcacion Recaptura Limpias", na = "NA",
  col_types = c("numeric", rep("text", 4), rep("numeric", 5), 
                rep("text", 4), rep("numeric", 12), rep("text", 3))))

head(sf_recaps)

## # A tibble: 6 x 29
##   `Orden original` Isla  Grupo GPS   Waypoint   Año   Mes   Día Latitud Longitud
##              <dbl> <chr> <chr> <chr> <chr>    <dbl> <dbl> <dbl>   <dbl>    <dbl>
## 1                1 Sant~ <NA>  <NA>  <NA>      2015     8    11  -0.819    -90.1
## 2                2 Sant~ <NA>  <NA>  <NA>      2015     8    13  -0.820    -90.1
## 3                3 Sant~ <NA>  <NA>  <NA>      2015     8    12  -0.819    -90.1
## 4                4 Sant~ <NA>  <NA>  <NA>      2015     8    11  -0.820    -90.1
## 5                5 Sant~ <NA>  <NA>  <NA>      2015     8    11  -0.822    -90.1
## 6                7 Sant~ <NA>  <NA>  <NA>      2015     8    11  -0.819    -90.1
## # ... with 19 more variables: `Número de PIT` <chr>, `PIT DPNG liberado` <chr>,
## #   PIT_final <chr>, `Número con Hierro` <chr>, `Largo Curvo (cm)` <dbl>,
## #   `Ancho Curvo (cm)` <dbl>, `Plastron (cm)` <dbl>, `Apertura Carapacho
## #   (cm)` <dbl>, `Peso (Kg)` <dbl>, Captura <dbl>, Recaptura <dbl>,
## #   Year_liberated <dbl>, LC_at_liberation <dbl>, Peso_at_liberation <dbl>,
## #   age_at_liberation <dbl>, age_at_recapture <dbl>, check_PIT <chr>,
## #   ...28 <chr>, Comentarios <chr>

We’ll change some column names and create some extra survey variables. I’ll clean everything in a long chunk (hidden) and create a new object for examining growth patterns.

We have some measurement errors and potential outliers in the data. We’ll label points as outliers according to a 3 * IQR rule, with quartiles specified separately along 2-cm length increments (for increments with 10 or more points).

We might have to manually label some additional measurements as outliers if they fall in an increment with a small sample size but are clearly off the length versus weight curve.

# get thresholds for extreme outliers (3 * IQR)
santafe.thresholds <- santafe.raw %>%
  mutate(lc_cat_2 = floor_any(LC_capture, 2)) %>%
  group_by(lc_cat_2) %>%
  summarise(Q3 = quantile(Peso_capture, 0.75, na.rm = T),
            Q1 = quantile(Peso_capture, 0.25, na.rm = T),
            IQR = Q3-Q1,
            upper = Q3+3*IQR,
            lower = Q1-3*IQR,
            n = n()) %>% ungroup()

# identify points beyond outlier thresholds
santafe.outliers <- santafe.raw %>%
  mutate(lc_cat_2 = floor_any(LC_capture, 2)) %>%
  left_join(santafe.thresholds, by = "lc_cat_2") %>%
  filter(Peso_capture > upper & n >= 10 | Peso_capture < lower & n >= 10 |
           Peso_capture > 1 & LC_capture < 20)

# number of Santa Fe outliers
nrow(santafe.outliers)

## [1] 71

ggplot(santafe.raw, aes(x = LC_capture, y = Peso_capture)) + 
  geom_point(alpha = 0.3, shape = 16) + 
  geom_point(data = santafe.outliers, aes(x = LC_capture, y = Peso_capture), 
             colour="red", fill = "red", shape = 16) + 
  theme_classic() + mythemes

Let’s omit those 71 outliers before modeling growth.

santafe.clean <- santafe.raw[santafe.raw$unique_id %notin% 
                               santafe.outliers$unique_id,]
santafe.clean$PIT_final <- as.factor(santafe.clean$PIT_final)

Here I’ll model the simple relationship between body size (LC) and age using generalized additive models (GAMs), with a random effect for tortoise ID (PIT tag). This will allow us to look at overall growth patterns, while also accounting for the variation in individual growth rates.

library(mgcv)
gam.larga <- bam(LC_capture ~ s(Age_actual) + s(PIT_final, bs = "re"), 
                 data = santafe.clean)
summary(gam.larga)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## LC_capture ~ s(Age_actual) + s(PIT_final, bs = "re")
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  32.2969     0.1784     181   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                   edf  Ref.df       F p-value    
## s(Age_actual)   6.399   7.496 6412.70  <2e-16 ***
## s(PIT_final)  539.585 550.000   49.26  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.977   Deviance explained = 98.3%
## fREML = 4220.7  Scale est. = 1.0414    n = 2143

library(tidymv)
length.plot.sf <- plot_smooths(model = gam.larga, series = Age_actual) + 
  geom_point(data = santafe.clean, 
             mapping = aes(x = Age_actual, y = LC_capture), 
             alpha = 0.1, shape = 16) + 
  geom_line(size = 0.5, col = "black") + 
  labs(y = "Curved carapace length (cm)", x = "Age (years)") + 
  scale_x_continuous(limits = c(4,14), breaks = c(4:14)) +
  theme_classic() + mythemes

length.plot.sf

Let’s do the same for tortoise weight.

gam.peso <- bam(Peso_capture ~ s(Age_actual) + s(PIT_final, bs="re"), 
                data = santafe.clean)
summary(gam.peso)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## Peso_capture ~ s(Age_actual) + s(PIT_final, bs = "re")
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.79166    0.07167    52.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                   edf  Ref.df       F p-value    
## s(Age_actual)   8.564   8.918 1400.53  <2e-16 ***
## s(PIT_final)  499.411 550.000   10.51  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.917   Deviance explained = 93.7%
## fREML = 3429.5  Scale est. = 0.80616   n = 2077

Let’s plot out the predicted relationship.

weight.plot.sf <- plot_smooths(model = gam.peso, series = Age_actual) + 
  geom_point(data = santafe.clean, 
             aes(x = Age_actual, y = Peso_capture), alpha = 0.1, shape = 16) + 
  geom_line(size = 0.5, col = "black") + labs(y = "Weight (kg)", x = "Age") + 
  scale_x_continuous(limits = c(4,14), breaks = c(4:14)) +
  theme_classic() + mythemes

weight.plot.sf

It is important to remember that we have a very small sample of individuals captured at 14 years old, (n = 5). It is unlikely that the tortoises on Santa Fe are shrinking as they get old. But it seems that some tortoises have remained small and experienced limited growth for their age.

Let’s put changes in length and weight on the same plot.

library(ggpubr)
ggarrange(length.plot.sf, weight.plot.sf, nrow = 2, common.legend = TRUE, 
          legend = "right",
          labels = c("Deviance explained = 98.3% \n \      R2-adj = 0.98", 
                     "Deviance explained = 93.7% \n \      R2-adj = 0.92"), 
          hjust = -0.3)

Body condition

What if we relate length and weight with each other (e.g., body condition)?

gam.largavpeso.sf <- bam(Peso_capture ~ s(LC_capture) + s(PIT_final, bs="re"), 
                         data = santafe.clean)
summary(gam.largavpeso.sf)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## Peso_capture ~ s(LC_capture) + s(PIT_final, bs = "re")
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.83472    0.01275   300.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                  edf Ref.df        F p-value    
## s(LC_capture)  7.735   8.57 6938.122  <2e-16 ***
## s(PIT_final)  28.648 550.00    0.056   0.178    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.967   Deviance explained = 96.8%
## fREML =   1788  Scale est. = 0.31742   n = 2077

largavpeso.sf.plot <-  
  plot_smooths(model = gam.largavpeso.sf, series = LC_capture) + 
  geom_point(data = santafe.clean, 
             mapping = aes(x = LC_capture, y = Peso_capture, fill = Cohort,
                           color = Cohort, shape = Cohort), 
             position = "jitter", alpha = 0.7) + 
  geom_line(size = 0.5, col = "black") +
  labs(y = "Weight (kg)", x = "Curved carapace length (cm)") + 
  scale_shape_manual(values = c(21, 22, 24)) +
  scale_color_manual(values = c("indianred4", "dodgerblue4", "goldenrod")) +
  scale_fill_manual(values = c("indianred4", "dodgerblue4", "goldenrod")) + 
  theme(legend.position = "top") + theme_classic() + mythemes

largavpeso.sf.plot

It doesn’t look like there is any between-cohort variation in body condition. All cohorts are evenly distributed along the fitted body condition curve.

We can confirm this by summarizing residual patterns. Let’s inspect a few things:

• Residuals by release cohort
• Residuals by elapsed time-since-release
• Residuals by time

body.res <-
  santafe.clean %>%
  filter(!is.na(LC_capture) & !is.na(Peso_capture)) %>%
  mutate(resid = gam.largavpeso.sf$residuals) %>%
  mutate(time_since_release = date_capture - date_firstmeasure,
         Cohort2 = as.factor(case_when(Cohort == "2015" ~ "Cohort 1",
                                       Cohort == "2017" ~ "Cohort 2",
                                       Cohort == "2019" ~ "Cohort 3")),
         release = ifelse(time_since_release == 0 | time_since_release == 77, 
                          "release", "recapture"),
         time_occ = case_when(Occasion == "1" ~ mean(dec.date[Occasion == "1"]),
                              Occasion == "2" ~ mean(dec.date[Occasion == "2"]),
                              Occasion == "3" ~ mean(dec.date[Occasion == "3"]),
                              Occasion == "4" ~ mean(dec.date[Occasion == "4"]),
                              Occasion == "5" ~ mean(dec.date[Occasion == "5"]),
                              Occasion == "6" ~ mean(dec.date[Occasion == "6"]),
                              Occasion == "7" ~ mean(dec.date[Occasion == "7"]),
                              Occasion == "8" ~ mean(dec.date[Occasion == "8"]),
                              Occasion == "9" ~ mean(dec.date[Occasion == "9"]),
                              Occasion == "10" ~ mean(dec.date[Occasion == "10"]
                                                      )))
                              
ggplot(body.res, aes(x = Cohort2, y = resid)) +
  stat_summary(fun.data = "mean_cl_normal",  geom = "pointrange") +
  geom_hline(aes(yintercept = 0), lty = "dashed") +
  ylab("Body condition residual") + xlab("Cohort") +
  theme_classic() + mythemes

ggplot(body.res, aes(x = time_since_release, y = resid)) +
  facet_wrap(~Cohort2, nrow = 3) +
  geom_smooth(method = "lm") +
  geom_point(shape = 16, alpha = 0.05) +
  geom_hline(aes(yintercept = 0), lty = "dashed") +
  ylab("Body condition residual") + xlab("Days since release") +
  theme_classic() + mythemes

body.res %>%
  group_by(time_occ, Cohort2) %>%
  summarise(resid = mean(resid)) %>%
  ggplot() +    
  geom_hline(aes(yintercept = 0), lty = "dashed", alpha = 0.4) +
  geom_point(data = body.res, aes(x = time_occ, y = resid), 
             shape = 16, alpha = 0.1, col = "grey50", position = "jitter") +
  geom_point(aes(x = time_occ, y = resid), color = "red", shape = "-", size = 6) +
  facet_wrap(~Cohort2, nrow = 3) + 
  ylab("Body condition residual") + xlab("Capture date") +
  theme_classic() + mythemes -> bc.res.plot

bc.res.plot

There don’t appear to be any differences in body condition between release cohorts. There also don’t appear to be any strong trends in body condition over time, except for a recent uptick (heavier) in the last year.

Tortoise morphology—Española

espanola.data <- read.csv("data/espanola_tortoise_data.csv")

# add unique id column
espanola.data$unique_id <- c(1:nrow(espanola.data))

Let’s first examine the data for potential outliers as we did before with the Santa Fe tortoises. We’ll constrain our Española data to be within the same age range of our Santa Fe tortoises. We’ll also omit data from 1980 to 1991 for comparing body condition, as the weight measurements during those years were filled with measurement or data entry errors that cannot be resolved.

espanola.raw <- 
  espanola.data[espanola.data$Year %notin% c(1980:1991) &
                  espanola.data$Age_capture >= min(santafe.clean$Age_actual) &
                  espanola.data$Age_capture <= max(santafe.clean$Age_actual),]

espanola.thresholds <- espanola.raw %>%
  mutate(lc_cat_2 = floor_any(LC_capture, 2)) %>%
  group_by(lc_cat_2) %>%
  summarise(Q3 = quantile(Peso_capture, 0.75, na.rm = T),
            Q1 = quantile(Peso_capture, 0.25, na.rm = T),
            IQR = Q3-Q1,
            upper = Q3+3*IQR,
            lower = Q1-3*IQR,
            n = n()) %>% ungroup()

espanola.outliers <- espanola.raw %>%
  mutate(lc_cat_2 = floor_any(LC_capture, 2)) %>%
  left_join(espanola.thresholds, by = "lc_cat_2") %>%
  filter(Peso_capture > upper & n >= 10 | Peso_capture < lower & n <= 10)

nrow(espanola.outliers)

## [1] 27

ggplot(espanola.raw, aes(x = LC_capture, y = Peso_capture)) + 
  geom_point(alpha = 0.3, shape = 16) +
  geom_point(data = espanola.outliers, aes(x=LC_capture, y = Peso_capture), 
             colour="red", fill = "red", shape = 16) + xlim(c(15,70)) +
  theme_classic() + mythemes

There are 27 obvious outliers here that we’ll remove.

espanola.clean <- 
  espanola.data[espanola.data$unique_id %notin% espanola.outliers$unique_id &
                  espanola.data$Year %notin% c(1980:1991) &
                  espanola.data$LC_capture < 70 &
                  espanola.data$Age_capture <= max(santafe.clean$Age_actual) &
                  espanola.data$Age_capture >= min(santafe.clean$Age_actual),]

espanola.clean <- espanola.clean[!is.na(espanola.clean$Year),]

Growth GAMs

Let’s combine our cleaned Santa Fe and Española datasets to model both populations together and display the regional growth contrasts.

espanola.clean$dec.date <- 
  decimal_date(as.Date(paste(espanola.clean$Year, 
                             espanola.clean$Month, 
                             espanola.clean$Year, 
                             sep = "-"), format = "%Y-%m-%d"))
espanola.clean$Age_actual <- espanola.clean$dec.date - espanola.clean$Birth_year
espanola.clean$mod.ID <- as.factor(espanola.clean$mod.ID)
espanola.clean$PIT <- as.factor(espanola.clean$PIT)

hood.data <- data.frame(
  dec.date = c(santafe.clean$dec.date, espanola.clean$dec.date),
  LC_capture = c(santafe.clean$LC_capture, espanola.clean$LC_capture),
  Peso_capture = c(santafe.clean$Peso_capture, espanola.clean$Peso_capture),
  Age_release = c(santafe.clean$Age_release, espanola.clean$Age_release),
  Age_capture = c(santafe.clean$Age_actual, espanola.clean$Age_actual),
  ID = as.factor(c(as.character(santafe.clean$PIT_final), 
                   as.character(espanola.clean$mod.ID))),
  Island = as.factor(c(rep("Santa Fe", nrow(santafe.clean)), 
                           rep("Española", nrow(espanola.clean)))))

# make island an ordered factor for the factor smooth interactions
hood.data$Island_ord <- ordered(hood.data$Island)

# summary of body condition data captures
hood.data %>%
  group_by(ID, Island) %>%
  summarise(n_raw = n()) %>%
  group_by(Island) %>%
  summarise(tortoises = length(unique(ID)),
            n = sum(n_raw),
            min_n = min(n_raw),
            mean_n = mean(n_raw),
            max_n = max(n_raw),
            sd_n = sd(n_raw)) %>% ungroup()

## # A tibble: 2 x 7
##   Island   tortoises     n min_n mean_n max_n  sd_n
##   <fct>        <int> <int> <int>  <dbl> <int> <dbl>
## 1 Española       680  1029     1   1.51     5 0.841
## 2 Santa Fe       551  2143     1   3.89     8 1.52

Let’s first look at the change in length with age.

gam.larga.hood <- bam(LC_capture ~ Island + s(Age_capture) + 
                        s(Age_capture, by = Island_ord) + 
                        s(ID, bs = "re"), data = hood.data)

summary(gam.larga.hood)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## LC_capture ~ Island + s(Age_capture) + s(Age_capture, by = Island_ord) + 
##     s(ID, bs = "re")
## 
## Parametric coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     36.4519     0.1703   214.1   <2e-16 ***
## IslandSanta Fe  -3.9214     0.2482   -15.8   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                        edf   Ref.df       F p-value    
## s(Age_capture)                       7.525    8.142 2109.92  <2e-16 ***
## s(Age_capture):Island_ordSanta Fe    6.860    7.561   51.09  <2e-16 ***
## s(ID)                             1124.533 1229.000   13.00  <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.964   Deviance explained = 97.7%
## fREML = 7732.1  Scale est. = 2.7004    n = 3172

# predict from model to plot curves for both populations
age.sim = rep(seq(min(hood.data$Age_capture), max(hood.data$Age_capture), 
                  length.out = 30), 2)

# create sequence of islands for prediction
island.sim = c(rep("Santa Fe", 30), rep("Española", 30))

# create new data frame with model covariates for prediction
newdat = data.frame(Age_capture = age.sim, Island = island.sim, 
                    Island_ord = island.sim)

# predict
hood.larga.pred <- predict.gam(gam.larga.hood, newdata = newdat, 
                               exclude = "s(ID)", type = "response", 
                               newdata.guaranteed = TRUE, se.fit=TRUE)

# put predicted values and error in new data frame for plotting
hood.larga <- data.frame(Island = island.sim,
                         Age = age.sim,
                         Pred = hood.larga.pred$fit,
                         SE = hood.larga.pred$se.fit)

# plot
hood.larga.plot <- ggplot(hood.larga, aes(x = Age, y = Pred, color = Island, 
                              fill = Island)) + 
  geom_ribbon(aes(ymin = Pred - 1.96*SE, ymax = Pred + 1.96*SE), 
              alpha = 0.2, color = "transparent") + xlim(4,15) + 
  geom_line(size = 1) + 
  geom_point(data = hood.data, inherit.aes = FALSE,
             aes(x = Age_capture, y = LC_capture, color = Island), 
             shape = 16, alpha = 0.2) +
  scale_x_continuous(limit = c(4,15), breaks = c(4:15)) +
  scale_color_manual(values = c("indianred4", "dodgerblue4")) + 
  scale_fill_manual(values = c("indianred4", "dodgerblue4")) +
  labs(y = "Curved carapace length (cm)", x = "Age (years)") + 
  theme_classic() + mythemes +
  theme(legend.position = "bottom")

hood.larga.plot

The juvenile tortoises on Santa Fe are smaller than their counterparts on Española. This could be because they were released as older and/or smaller juveniles on Santa Fe, thus acclimating to the island ecosystem at a later developmental stage. The Santa Fe tortoises seem to catch up by age 12 though.

Body condition

Let’s model the relationship between length and weight and compare that body condition function to the Santa Fe tortoise data.

hood.bc.gam <- bam(Peso_capture ~ Island + s(LC_capture) +
                   s(LC_capture, by = Island_ord) + 
                   s(ID, bs = "re"), data = hood.data)

summary(hood.bc.gam)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## Peso_capture ~ Island + s(LC_capture) + s(LC_capture, by = Island_ord) + 
##     s(ID, bs = "re")
## 
## Parametric coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     4.53255    0.03469 130.664   <2e-16 ***
## IslandSanta Fe  0.05898    0.04221   1.397    0.162    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                        edf   Ref.df       F p-value    
## s(LC_capture)                    8.0476501    8.700 3797.69  <2e-16 ***
## s(LC_capture):Island_ordSanta Fe 3.4075998    4.195   22.77  <2e-16 ***
## s(ID)                            0.0008945 1176.000    0.00   0.576    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.95   Deviance explained =   95%
## fREML = 4189.7  Scale est. = 0.91664   n = 3028

# create length sequence for prediction
larga.sim = c(rep(seq(min(santafe.clean$LC_capture), 
                max(santafe.clean$LC_capture), length.out = 100), 2))

# create sequence of islands for prediction
island.sim = c(rep("Santa Fe", 100), rep("Española", 100))

# create new data frame with model covariates for prediction
newdat = data.frame(LC_capture = larga.sim, Island_ord = island.sim, 
                    Island = island.sim)

# predict
hood.bc.pred <- predict.gam(hood.bc.gam, newdata = newdat,
                            exclude = "s(ID)", newdata.guaranteed = TRUE, 
                            type = "response", se.fit=TRUE)

# put predicted values and error in new data frame for plotting
hood.bc <- data.frame(cbind(island.sim), 
                      as.numeric(as.character(larga.sim)), 
                      as.numeric(as.character(hood.bc.pred$fit)),
                      as.numeric(as.character(hood.bc.pred$se.fit)))
colnames(hood.bc) <- c("Island", "larga", "peso", "SE")

# plot
hood.bc.plot <- ggplot(hood.bc, 
                       aes(x = larga, y = peso, color = Island, fill = Island)) + 
  geom_ribbon(aes(ymin = peso - 1.96*SE, ymax = peso + 1.96*SE), 
              color = "transparent", alpha = 0.2) +
  geom_point(inherit.aes = FALSE, 
             data = hood.data[hood.data$Island == "Santa Fe",], 
             mapping = aes(x = LC_capture, y = Peso_capture), 
             position = "jitter", shape = 16, alpha = 0.2, col = "#00BFC4") + 
  geom_point(inherit.aes = FALSE, 
             data = hood.data[hood.data$Island == "Española",], 
             mapping = aes(x = LC_capture, y = Peso_capture), 
             position = "jitter", shape = 16, alpha = 0.2, col = "#F8766D") + 
  geom_line(size = 1.1) +
  scale_color_manual(values = c("indianred4", "dodgerblue4")) + 
  scale_fill_manual(values = c("indianred4", "dodgerblue4")) +
  labs(y = "Weight (kg)", x = "Curved carapace length (cm)") + 
  theme_classic() + mythemes + theme(legend.position = "bottom") + 
  xlim(min(santafe.clean$LC_capture), max(santafe.clean$LC_capture)) + 
  ylim(c(0,22))

hood.bc.plot

It looks like the Santa Fe and Española tortoise populations are showing similar morphological patterns, despite the Santa Fe tortoises being smaller at given ages. There is a slight divergence in body condition that begins at about 40 cm, where tortoises on Santa Fe are a bit heavier for a given size than those on Española.

Let’s export our body condition model table to a csv file.

bc.model.summary <- summary(hood.bc.gam)
write.csv(bc.model.summary$p.table, "data/bc_mod_parametric.csv")
write.csv(bc.model.summary$s.table, "data/bc_mod_smooth.csv")

Let’s look at the data just one other way with box plots.

hood.data$LC_class <- as.factor(floor_any(hood.data$LC_capture, 10))

ggplot(na.omit(hood.data[hood.data$LC_class == "20" | 
                           hood.data$LC_class == "30" |
                           hood.data$LC_class == "40" | 
                           hood.data$LC_class == "50",]), 
       aes(x = LC_class, y = Peso_capture, color = Island)) +
  geom_boxplot(outlier.alpha = 0.5, outlier.shape = 16) + 
  labs(y = "Weight (kg)", x = "Curved carapace length class (cm)") +
  scale_color_manual(values = c("indianred4", "dodgerblue4")) +
  guides(color = guide_legend(title = "Island")) + 
  theme_classic() + mythemes + 
  theme(legend.position = "bottom")

These boxplots indicate that any small divergence in body condition specified by the GAM, is likely negligible.

Tortoise growth rates

Let’s now compare the actual somatic growth rates for tortoises on Santa Fe and Española, using intermediate length as a predictor.

I’ll follow a few protocols to make our Santa Fe and Española data more comparable and limit data errors: (1) I omit all growth intervals less than 1 year or greater than 5 years (the latter being the amount of time elapsed since tortoises were introduced to Santa Fe); (2) I apply some filtering rules to omit some questionable measurements that are likely products of data recording and entering errors; and (3) I truncate tabulated growth rates at negative and positive extremes of -2.5 cm / yr and 10 cm / yr.

# first get reduced data frame with:
## (1) just individuals captured at least twice, and 
## (2) containing size data
growth.input <- hood.data %>%
  filter(is.na(LC_capture) == FALSE) %>%
  group_by(Island, ID) %>%
  filter(n() > 1) %>%
  mutate(cap_date = dec.date) %>%
  arrange(cap_date) %>%
  ungroup() %>%
  mutate(unique_id = c(1:length(dec.date))) %>% 
  as.data.frame()

# function to calculate growth rates
growth.tabulate <- function(data){
  ## CLEANING LOOP
  clean_data <- NULL
  # nest by island
  for(Island in unique(data$Island)){
    # nest by tortoise ID
    for(ID in unique(data$ID[data$Island %in% Island])){
      tdata <- data[data$Island %in% Island & data$ID %in% ID,]
      final_cap = last(tdata$unique_id)
      current_cap = 1
      while(current_cap != final_cap){
        for(cap in 2:nrow(tdata)){
          current_cap = tdata$unique_id[cap]
          if(
            # If recap is too soon after the previous capture...
            tdata$cap_date[cap] - tdata$cap_date[cap-1] < 1 |
            # or shrinks
            tdata$LC_capture[cap] / tdata$LC_capture[cap-1] < 0.95 |
            # or grows quicker than 10 cm / yr
            (tdata$LC_capture[cap] - tdata$LC_capture[cap-1]) / 
            (tdata$cap_date[cap] - tdata$cap_date[cap-1]) > 10) {
            # remove cap 
            tdata <- tdata[-cap,]
            break
          }
        }
      }
      clean_data <- bind_rows(clean_data, tdata)
    }
  }
  #### CALCULATE GROWTH RATES FOR REMAINING INTERVALS ####
  growth_data <- NULL
  clean_data <- clean_data %>%
    group_by(Island, ID) %>%
    filter(n() > 1) %>% ungroup() %>%
    as.data.frame()
  # construct rows for growth dataset from clean data
  for(Island in unique(clean_data$Island)){
    # nest by tortoise ID
    for(ID in unique(clean_data$ID[clean_data$Island %in% Island])){
      tdata <- clean_data[clean_data$Island %in% Island & clean_data$ID %in% ID,]
      for(cap in 2:nrow(tdata)){
        new.df <- data.frame(
          # island
          Island = Island,
          # ID of tortoise
          ID = ID,
          # capture date
          cap_year = tdata$cap_date[cap-1],
          # recapture date
          recap_year = tdata$cap_date[cap],
          # time between captures
          years_between = tdata$cap_date[cap] - tdata$cap_date[cap-1],
          # mid-year between captures
          midyear = mean(c(tdata$cap_date[cap], tdata$cap_date[cap-1])),
          # original length
          cap_lc = tdata$LC_capture[cap-1],
          # recapture length
          recap_lc = tdata$LC_capture[cap],
          # size difference between captures
          delta_lc = tdata$LC_capture[cap] - tdata$LC_capture[cap-1],
          # mid-size between captures
          mid_lc = mean(c(tdata$LC_capture[cap], tdata$LC_capture[cap-1])),
          # mid age
          mid_age = mean(c(tdata$Age_capture[cap], tdata$Age_capture[cap-1])),
          # growth rate
          growth_cm_yr = (tdata$LC_capture[cap] - tdata$LC_capture[cap-1])/
            (tdata$cap_date[cap] - tdata$cap_date[cap-1]),
          stringsAsFactors = FALSE)
        growth_data <- bind_rows(growth_data, new.df)
      }
    }
  }
  return(growth_data)
}

# run growth function
growth.output <- growth.tabulate(growth.input)

# filter out additional growth intervals
growth.dat <- growth.output %>%
  filter(years_between <= 5) %>%
  mutate(ID = as.factor(ID),
         Island = as.factor(Island),
         growth_rate_pc = p.rank(growth_cm_yr),
         growth_rate_final = growth_cm_yr,
         growth_rate_final = ifelse(growth_cm_yr <= -2.5 | 
                                      growth_cm_yr >= 10, NA, growth_rate_final))

Let’s take a quick look at a summary of our growth dataset.

growth.dat %>%
  group_by(Island) %>%
  summarise(mean_growth = mean(growth_rate_final),
            sd_growth = sd(growth_rate_final)) -> mean.growth.rates

growth.dat %>%
  group_by(ID, Island) %>%
  summarise(n_raw = n()) %>%
  group_by(Island) %>%
  summarise(tortoises = length(unique(ID)),
            n = sum(n_raw),
            min_n = min(n_raw),
            mean_n = mean(n_raw),
            max_n = max(n_raw),
            sd_n = sd(n_raw)) %>%
  left_join(mean.growth.rates, by = "Island") %>%
  mutate(se = sd_growth/sqrt(n)) %>%
  ungroup()

## # A tibble: 2 x 10
##   Island   tortoises     n min_n mean_n max_n  sd_n mean_growth sd_growth     se
##   <fct>        <int> <int> <int>  <dbl> <int> <dbl>       <dbl>     <dbl>  <dbl>
## 1 Española       174   218     1   1.25     3 0.474        4.39      1.58 0.107 
## 2 Santa Fe       425   749     1   1.76     3 0.689        3.99      1.01 0.0370

Okay now let’s run a somatic growth model for just Santa Fe.

santafe.growth.dat <- growth.dat %>%
  filter(Island == "Santa Fe") %>%
  droplevels()

santafe.growth.gam <- bam(growth_rate_final ~ s(mid_lc) + s(ID, bs="re"), 
                          data = santafe.growth.dat)

summary(santafe.growth.gam)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## growth_rate_final ~ s(mid_lc) + s(ID, bs = "re")
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.98613    0.02984   133.6   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                 edf  Ref.df     F p-value    
## s(mid_lc) 4.9220490   6.068 66.82  <2e-16 ***
## s(ID)     0.0001219 424.000  0.00   0.592    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.351   Deviance explained = 35.6%
## fREML = 919.95  Scale est. = 0.66683   n = 749

larga.sim = seq(min(na.omit(santafe.growth.dat$mid_lc)), 
                max(na.omit(santafe.growth.dat$mid_lc)), length.out = 100)

# santa fe prediction
newdat <- data.frame(mid_lc = larga.sim)
santafe.pred <- predict.gam(santafe.growth.gam, newdata = newdat, 
                            exclude = "s(ID)", newdata.guaranteed = TRUE,
                            type = "response", se.fit=TRUE)
santafe.pred <- data.frame(cbind(larga.sim, santafe.pred$fit, 
                                 santafe.pred$se.fit))
colnames(santafe.pred) <- c("larga", "rate", "SE")

### PLOT ###
santafe.growth.plot <-  ggplot(santafe.pred, aes(x = larga, y = rate)) + 
  geom_point(inherit.aes = FALSE, data = santafe.growth.dat, 
             mapping = aes(x = mid_lc, y = growth_cm_yr), 
             position = "jitter", alpha = 0.1) + geom_line(size = 1.1) + 
  geom_line(aes(y=rate - 2*SE), linetype = "dashed") + 
  geom_line(aes(y=rate + 2*SE), linetype = "dashed") + 
  geom_line(mapping = aes(y = 0), linetype = "dashed", col = "black") + 
  labs(y = expression(paste("Growth rate (cm yr"^{-1},")")), 
       x = "Intermediate curved carapace length (cm)") + 
  theme_classic() + mythemes +
  scale_shape_manual(values=c(2,1)) + ylim(-2.5, 10)

santafe.growth.plot 

The Santa Fe tortoises are growing steadily.

Let’s examine the residuals over time.

santafe.cohorts <- santafe.raw %>%
  group_by(PIT_final) %>%
  summarise(ID = unique(PIT_final),
            Cohort = unique(Cohort))

growth.res <-
  santafe.growth.dat %>%
  filter(!is.na(growth_rate_final)) %>%
  mutate(resid = santafe.growth.gam$residuals) %>%
  left_join(santafe.cohorts, by = "ID") %>%
  mutate(Cohort2 = case_when(Cohort == "2015" ~ "1 (2015)",
                             Cohort == "2017" ~ "2 (2017)",
                             Cohort == "2019" ~ "3 (2019"))

growth.res.plot <- 
  ggplot(growth.res, aes(x = midyear, y = resid)) +
  geom_point(shape = 16, alpha = 0.2) +
  geom_smooth(method = "lm") + scale_y_continuous(breaks = c(-3,0,3)) +
  geom_hline(aes(yintercept = 0), lty = "dashed") +
  ylab("Growth residual") + xlab("Intermediate capture date") +
  theme_classic() + mythemes

growth.res.plot

There doesn’t appear to be any residual trend over time, indicating that growth rates are stable for the Santa Fe tortoise population.

espanola.growth.dat <- growth.dat %>%
  filter(Island == "Española") %>%
  droplevels()

espanola.growth.gam <- bam(growth_rate_final ~ s(mid_lc) + s(ID, bs="re"), 
                           data = espanola.growth.dat)

summary(espanola.growth.gam)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## growth_rate_final ~ s(mid_lc) + s(ID, bs = "re")
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.36640    0.09874   44.22   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf  Ref.df      F p-value    
## s(mid_lc)  4.546   5.358 12.834 5.1e-11 ***
## s(ID)     57.058 173.000  0.512 0.00205 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.455   Deviance explained =   61%
## fREML =  384.3  Scale est. = 1.3523    n = 218

larga.sim = seq(min(espanola.growth.dat$mid_lc), 
                max(espanola.growth.dat$mid_lc), length.out = 100)

# espanola prediction
newdat <- data.frame(mid_lc = larga.sim)
espanola.pred <- predict.gam(espanola.growth.gam, newdata = newdat, 
                             newdata.guaranteed = TRUE,
                             exclude = "s(ID)", type = "response", 
                             se.fit=TRUE)
espanola.pred <- data.frame(cbind(larga.sim, espanola.pred$fit, 
                                  espanola.pred$se.fit))
colnames(espanola.pred) <- c("larga", "rate", "SE")

### PLOT ###
espanola.growth.plot <-  ggplot(espanola.pred, aes(x = larga, y = rate)) + 
  geom_point(inherit.aes = FALSE, data = espanola.growth.dat, 
             mapping = aes(x = mid_lc, y = growth_rate_final), 
             position = "jitter", alpha = 0.2) + geom_line(size = 1.1) + 
  geom_line(aes(y=rate - 2*SE), linetype = "dashed") + 
  geom_line(aes(y=rate + 2*SE), linetype = "dashed") + 
  geom_line(mapping = aes(y = 0), linetype = "dashed", col = "black") + 
  labs(y = expression(paste("Growth rate (cm yr"^{-1},")")), 
       x = "Intermediate curved carapace length (cm)") + 
  theme_classic() + mythemes +
  scale_shape_manual(values=c(2,1)) + ylim(-2.5, 10)

espanola.growth.plot

Let’s compare Santa Fe and Española growth rates in the same model.

growth.dat$Island_ord = ordered(growth.dat$Island)

hood.growth.gam <- bam(growth_rate_final ~ Island + s(mid_lc) + 
                         s(mid_lc, by = Island_ord) + 
                         s(ID, bs="re"), data = growth.dat)

summary(hood.growth.gam)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## growth_rate_final ~ Island + s(mid_lc) + s(mid_lc, by = Island_ord) + 
##     s(ID, bs = "re")
## 
## Parametric coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     4.59252    0.07545  60.866  < 2e-16 ***
## IslandSanta Fe -0.56171    0.08451  -6.647 5.19e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                                 edf  Ref.df      F  p-value    
## s(mid_lc)                     5.731   6.904 35.712  < 2e-16 ***
## s(mid_lc):Island_ordSanta Fe  1.000   1.000 67.647 6.26e-16 ***
## s(ID)                        60.559 597.000  0.114   0.0697 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.358   Deviance explained = 40.3%
## fREML = 1358.7  Scale est. = 0.88667   n = 967

There is a difference in growth rates between the two populations.

Let’s export this model table to a csv.

growth.model.summary <- summary(hood.growth.gam)
write.csv(growth.model.summary$p.table, "data/growth_mod_parametric.csv")
write.csv(growth.model.summary$s.table, "data/growth_mod_smooth.csv")

Now let’s plot out the predicted growth rates for each population.

age.sim = rep(c(seq(min(na.omit(growth.dat$mid_age)), 
                max(na.omit(growth.dat$mid_age)), length.out = 100)),2)

length.sim = c(seq(min(growth.dat$mid_lc[growth.dat$Island == "Santa Fe"]), 
                max(growth.dat$mid_lc[growth.dat$Island == "Santa Fe"]), 
                length.out = 100),
              seq(min(growth.dat$mid_lc[growth.dat$Island == "Española"]), 
                max(growth.dat$mid_lc[growth.dat$Island == "Española"]), 
                length.out = 100))

newdat = data.frame(mid_lc = length.sim,
                    Island = as.factor(c(rep("Santa Fe", 100), 
                                         rep("Española", 100))),
                    Island_ord = as.factor(c(rep("Santa Fe", 100), 
                                             rep("Española", 100))))

hood.pred <- predict.gam(hood.growth.gam, newdata = newdat, 
                         newdata.guaranteed = TRUE,
                             exclude = "s(ID)", type = "response", se.fit=TRUE)
hood.pred <- data.frame(length = length.sim, 
                        Island = c(rep("Santa Fe", 100), rep("Española", 100)), 
                        rate = hood.pred$fit, 
                        SE = hood.pred$se.fit)

hood.growth.plot <- ggplot(hood.pred, 
                           aes(x = length, y = rate, 
                               fill = Island, color = Island)) + 
  geom_point(inherit.aes = FALSE, 
             data = growth.dat[growth.dat$Island == "Santa Fe",], 
             mapping = aes(x = mid_lc, y = growth_rate_final), 
             position = "jitter", shape = 16, alpha = 0.2, col = "#00BFC4") + 
  geom_point(inherit.aes = FALSE, 
             data = growth.dat[growth.dat$Island == "Española",], 
             mapping = aes(x = mid_lc, y = growth_rate_final), 
             position = "jitter", shape = 16, alpha = 0.2, col = "#F8766D") + 
  geom_ribbon(aes(ymin = rate - 1.96*SE, ymax = rate + 1.96*SE), 
              color = "transparent", alpha = 0.2) +
  geom_line(size = 1.1) + 
  scale_color_manual(values = c("indianred4", "dodgerblue4")) +
  scale_fill_manual(values = c("indianred4", "dodgerblue4")) +
  labs(y = expression(paste("Growth rate (cm yr"^{-1},")")), 
       x = "Intermediate length (cm)") + theme_classic() + mythemes +
  ylim(0, 7.5) + theme(legend.position = "bottom")

hood.growth.plot

There are in fact some differences in the growth rates between tortoises on Santa Fe and Española. The Santa Fe tortoises begin with slower growth rates than those on Española. This could possibly be explained by the harsher environment on Santa Fe. Juvenile tortoises may have more limited foraging opportunities during the day in the hot season because of there is less cover. Release ages could also play a role, as Santa Fe tortoises were on average older upon release than Española tortoises. Tortoises may require a few years to acclimate to their environment after being repatriated.

After they exceed about 40 cm in length, the Santa Fe tortoises begin to growing faster than their counterparts on Española. This would make sense, considering the greater food resources on Santa Fe. There might simply be more food for them to eat.

Of course, climate may play an important role in this contrast. The Española tortoise program spanned almost 50 years from 1975 to present. The Santa Fe program did not begin until 2015. The different time frames mean that we are capturing growth during different periods of climate variation that have unclear effects on tortoise growth.

Let’s create a composite growth figure to include in the manuscript.

growth.fig <- 
  ggarrange(hood.bc.plot, hood.growth.plot, bc.res.plot, growth.res.plot,
            nrow = 2, ncol = 2, common.legend = TRUE, legend = "top",
            labels = c("a", "b", "c", "d"), label.x = c(0.15, 0.15, 0.15, 0.15))
growth.fig

Survival

---

Model preparation

Here we’ll use capture-mark-recapture population models (i.e., Cormack-Jolly-Seber or CJS models) to get an estimate of survival rates of the three release cohorts of tortoises on Santa Fe.

First we need to reformat the mark-recapture data to create individual encounter histories for program MARK.

## Aggregate by tag/mark ID to create annual encounter histories
library(reshape2)
santafe.ch <- santafe.raw %>%
  dplyr::select(c("PIT_final", "Occasion", "LC_capture", "Age_actual", 
           "Age_release", "LC_release", "Peso_release", "Cohort")) %>%
  mutate(PIT = as.factor(PIT_final),
         Cohort = as.factor(Cohort)) %>%
  group_by(PIT, Occasion, Cohort) %>%
  summarise_all(mean) %>%
  dcast(PIT + Age_release + LC_release + Peso_release + Cohort ~ Occasion) %>%
  mutate_at(c(as.character(1:10)), ~ifelse(is.na(.), 0, 1))
  
colnames(santafe.ch) <- c("PIT", "age_release", "length", "weight", 
                          "release_cohort",  "T0", "T0_17", "T1", "T1_83",
                          "T2", "T3", "T3_67", "T3_84", "T4_17", "T4_75")

# aggregate encounter history and reorder columns for input to MARK
santafe.ch <- 
  data.frame(ch = paste(santafe.ch$T0, santafe.ch$T0_17, santafe.ch$T1, 
                        santafe.ch$T1_83, santafe.ch$T2, santafe.ch$T3,
                        santafe.ch$T3_67, santafe.ch$T3_84,
                        santafe.ch$T4_17, santafe.ch$T4_75, sep = ""), 
             santafe.ch[,c(2:5)])

## write as a .txt file 
write.table(santafe.ch, "data/santafe_ch.txt", sep = "\t", col.names = TRUE, 
            row.names = FALSE, quote=FALSE)

We’ll use that text file that I just exported to set up the input data.

library(RMark)
tortoises <- import.chdata("data/santafe_ch.txt", header = TRUE, 
                               field.types=c("n", "n", "n", "f")) 

effortcov <- data.frame(read.csv("data/tortoise_survey_effort.csv"))

Now we’ll process the input data for CJS. Because there were uneven time intervals between tortoise surveys we’ll have to be careful here and specify the exact amount of time between surveys for the models to estimates annual survival properly.

# make process data
tortoises$age_release <- as.factor(tortoises$age_release)
tortoises.process <- 
  process.data(tortoises,model="CJS",begin.time=0,
               time.intervals=c(0.17, 0.83, 0.83, 0.17, 
                                1.00, 0.67, 0.17, 0.33, 0.58), 
               groups = c("release_cohort", "age_release"), age.var = 2,
               initial.ages = c(4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5))
 
library(kableExtra)
kable(tortoises.process$data, "html", 
      caption = "Tortoise capture data in Santa Fe") %>%
  kable_styling(bootstrap_options = c("striped", "condensed")) %>% 
  scroll_box(height = "300px")

Tortoise capture data in Santa Fe

ch	age_release	length	weight	release_cohort	group
1000100100	5.5	24.70000	1.450000	2015	3
1100110101	5.5	26.10000	1.800000	2015	3
1100100110	5.5	23.10000	0.800000	2015	3
1100110111	5.5	32.60000	1.000000	2015	3
1010100100	4.5	25.00000	1.100000	2015	1
1110000000	7.5	35.10000	3.700000	2015	9
1100000100	6.5	27.00000	1.600000	2015	6
1110110111	7.5	34.40000	3.800000	2015	9
1110100000	6.5	31.90000	3.200000	2015	6
1000010100	4.5	27.00000	1.600000	2015	1
1110110100	4.5	24.30000	1.250000	2015	1
1100010101	5.5	26.50000	1.700000	2015	3
1010010000	5.5	23.90000	1.200000	2015	3
1100010010	7.5	33.70000	2.400000	2015	9
1110110000	7.5	27.20000	1.400000	2015	9
1000110100	4.5	25.10000	1.300000	2015	1
1010110110	5.5	24.60000	1.400000	2015	3
1110110101	4.5	25.00000	1.250000	2015	1
1110010000	6.5	27.20000	2.700000	2015	6
1110110111	5.5	24.10000	1.200000	2015	3
1110110000	7.5	26.30000	1.200000	2015	9
1110010100	4.5	24.00000	1.250000	2015	1
1000000000	6.5	31.50000	2.800000	2015	6
1110110001	7.5	27.80000	1.700000	2015	9
1110110110	7.5	33.10000	3.300000	2015	9
1010010001	4.5	24.50000	1.200000	2015	1
1000010100	6.5	22.60000	1.100000	2015	6
1010010011	6.5	28.60000	2.000000	2015	6
1100110110	4.5	26.10000	1.500000	2015	1
1100000011	6.5	30.10000	2.300000	2015	6
1010110010	4.5	24.80000	1.300000	2015	1
1000010110	5.5	24.50000	1.150000	2015	3
1000000000	6.5	24.50000	1.300000	2015	6
1010110100	4.5	23.60000	1.200000	2015	1
1110010110	7.5	33.50000	3.200000	2015	9
1100100110	7.5	31.50000	2.500000	2015	9
1010010110	5.5	25.10000	1.150000	2015	3
1010110010	5.5	24.00000	1.300000	2015	3
1010010000	6.5	27.50000	2.100000	2015	6
1010100110	6.5	26.90000	1.700000	2015	6
1110110100	6.5	24.90000	1.400000	2015	6
1110100000	7.5	29.50000	2.400000	2015	9
1110110110	5.5	25.30000	1.500000	2015	3
1010100111	5.5	26.80000	1.700000	2015	3
1110110111	5.5	26.20000	1.400000	2015	3
1010110011	5.5	26.10000	1.500000	2015	3
1110000000	7.5	33.20000	3.100000	2015	9
0001110100	5.5	26.50000	1.750000	2017	4
1110110111	7.5	34.10000	3.600000	2015	9
1010010100	6.5	28.40000	2.400000	2015	6
1110100100	7.5	30.10000	2.300000	2015	9
1110000101	7.5	33.30000	3.300000	2015	9
1110110010	7.5	31.00000	2.700000	2015	9
1100110111	6.5	30.30000	2.600000	2015	6
1100100111	4.5	23.60000	1.300000	2015	1
1110110101	7.5	32.00000	2.800000	2015	9
1010110110	7.5	24.80000	1.300000	2015	9
1010010100	6.5	27.80000	2.000000	2015	6
1110010000	6.5	30.50000	2.700000	2015	6
1110110100	6.5	26.20000	1.500000	2015	6
1110000110	6.5	32.00000	3.050000	2015	6
1110110101	5.5	24.00000	1.200000	2015	3
1010110000	7.5	29.20000	1.900000	2015	9
1010010101	6.5	28.80000	2.250000	2015	6
1110110001	4.5	25.50000	1.300000	2015	1
1010100000	4.5	26.60000	1.600000	2015	1
1110110011	6.5	30.10000	2.400000	2015	6
1010110111	4.5	23.90000	1.200000	2015	1
1010110101	5.5	25.90000	1.600000	2015	3
1110110111	7.5	36.30000	1.200000	2015	9
1010110101	6.5	32.00000	3.000000	2015	6
1110000000	8.5	34.00000	3.500000	2015	12
1110010100	4.5	25.00000	1.200000	2015	1
1110010010	7.5	33.50000	2.800000	2015	9
1000000000	5.5	23.20000	1.000000	2015	3
1110100100	5.5	25.90000	1.650000	2015	3
1110100010	6.5	30.30000	2.750000	2015	6
1110010111	6.5	31.10000	2.750000	2015	6
1000000000	5.5	25.10000	1.100000	2015	3
1110010010	7.5	31.60000	2.700000	2015	9
1010110100	5.5	23.90000	1.200000	2015	3
1010010001	7.5	18.50000	7.000000	2015	9
1110010001	6.5	31.00000	2.700000	2015	6
1100010010	6.5	29.40000	2.500000	2015	6
1110110010	7.5	33.40000	3.300000	2015	9
1110000111	7.5	34.70000	3.700000	2015	9
1110110111	4.5	25.10000	1.400000	2015	1
1110110101	5.5	24.50000	1.300000	2015	3
0001110101	5.5	26.70000	1.611000	2017	4
1110000001	6.5	26.50000	1.800000	2015	6
1110000100	7.5	28.00000	1.800000	2015	9
1110110111	7.5	29.80000	2.300000	2015	9
1110110100	7.5	34.50000	3.700000	2015	9
1110100100	7.5	32.30000	2.600000	2015	9
1010110010	6.5	28.50000	2.300000	2015	6
1010000000	7.5	31.70000	2.700000	2015	9
1110100000	7.5	32.70000	2.700000	2015	9
0001010101	5.5	26.40000	1.669000	2017	4
1100000011	6.5	29.50000	2.100000	2015	6
1110100010	7.5	35.00000	3.900000	2015	9
1010110000	7.5	23.40000	1.300000	2015	9
1010000000	5.5	27.70000	1.900000	2015	3
1110110010	6.5	31.90000	2.950000	2015	6
1010010000	5.5	27.60000	1.850000	2015	3
1000100100	6.5	28.00000	2.100000	2015	6
1000000010	7.5	29.10000	2.100000	2015	9
1010110111	5.5	23.90000	1.200000	2015	3
1110110101	4.5	25.40000	1.500000	2015	1
1000100000	7.5	32.90000	2.800000	2015	9
1100000000	4.5	23.50000	1.150000	2015	1
1010100000	4.5	24.80000	1.300000	2015	1
1010100100	6.5	28.30000	1.850000	2015	6
1000000101	4.5	25.50000	1.550000	2015	1
1010110110	6.5	27.00000	1.700000	2015	6
1000110010	4.5	25.10000	1.500000	2015	1
1110110000	7.5	34.40000	3.900000	2015	9
1000010011	5.5	24.20000	1.300000	2015	3
1000100110	5.5	25.50000	1.600000	2015	3
1010000100	6.5	30.20000	2.150000	2015	6
1010110110	9.5	22.50000	0.950000	2015	14
0001010100	5.5	26.70000	1.634000	2017	4
1000110100	6.5	26.40000	2.800000	2015	6
1000000000	4.5	25.10000	1.450000	2015	1
1110110000	7.5	35.00000	4.300000	2015	9
1110110110	4.5	24.10000	1.200000	2015	1
1100010110	6.5	25.00000	1.400000	2015	6
1110110100	6.5	29.40000	2.400000	2015	6
1010110110	4.5	25.20000	1.400000	2015	1
1110110100	7.5	35.50000	3.500000	2015	9
1000110000	4.5	24.40000	1.250000	2015	1
1110000100	5.5	24.80000	1.050000	2015	3
1010010000	5.5	28.10000	2.200000	2015	3
1110110000	10.5	33.10000	2.800000	2015	15
1110110110	5.5	29.90000	0.900000	2015	3
0001110100	5.5	26.70000	1.521000	2017	4
1010110100	4.5	26.10000	1.500000	2015	1
1010110101	7.5	30.30000	2.400000	2015	9
1010010110	7.5	30.80000	2.700000	2015	9
1100000000	5.5	28.90000	2.200000	2015	3
1110110110	4.5	25.20000	1.500000	2015	1
1110110000	4.5	24.90000	1.500000	2015	1
1010010000	6.5	23.20000	1.100000	2015	6
1110110110	4.5	25.40000	1.450000	2015	1
1010010000	7.5	29.00000	1.800000	2015	9
1010110000	5.5	23.60000	0.900000	2015	3
1110010100	7.5	32.80000	2.300000	2015	9
1010110101	5.5	24.00000	1.200000	2015	3
1010110001	6.5	31.10000	2.750000	2015	6
1110110110	7.5	34.60000	3.600000	2015	9
1110110111	5.5	27.30000	2.000000	2015	3
1000000000	9.5	20.60000	0.800000	2015	14
1110110110	7.5	33.80000	3.200000	2015	9
1110010000	4.5	23.90000	1.000000	2015	1
1100000000	4.5	24.30000	1.200000	2015	1
1100000000	5.5	24.50000	1.300000	2015	3
1100100000	9.5	34.10000	3.400000	2015	14
1000010110	4.5	25.20000	1.250000	2015	1
1010100000	6.5	31.50000	2.900000	2015	6
1010110110	5.5	23.60000	1.300000	2015	3
1000110100	5.5	29.10000	2.000000	2015	3
1000110000	4.5	23.50000	1.100000	2015	1
1000010110	6.5	27.10000	1.950000	2015	6
1110110110	7.5	35.50000	3.050000	2015	9
1110110101	7.5	25.80000	1.500000	2015	9
1000010110	6.5	26.80000	1.700000	2015	6
1110110000	7.5	35.70000	1.700000	2015	9
1110000000	8.5	36.00000	4.800000	2015	12
1000000010	6.5	30.40000	2.600000	2015	6
1110110101	5.5	25.50000	1.500000	2015	3
1010000000	4.5	24.00000	1.200000	2015	1
1110100000	7.5	31.70000	2.800000	2015	9
1110100100	5.5	29.60000	2.250000	2015	3
1010000010	6.5	25.20000	1.300000	2015	6
1010110100	4.5	23.70000	1.050000	2015	1
1110010001	7.5	32.00000	3.300000	2015	9
1110110001	7.5	34.70000	3.500000	2015	9
1110110001	7.5	32.70000	3.000000	2015	9
1010000000	7.5	29.20000	2.200000	2015	9
1110110111	4.5	23.60000	1.100000	2015	1
1110100111	4.5	23.80000	1.300000	2015	1
1000000000	5.5	23.70000	1.050000	2015	3
1110110110	4.5	24.10000	1.200000	2015	1
1110100011	4.5	23.80000	1.200000	2015	1
1010100000	4.5	25.30000	1.300000	2015	1
1010100000	4.5	24.90000	1.550000	2015	1
1110110110	5.5	25.20000	1.500000	2015	3
1010110110	6.5	30.60000	2.800000	2015	6
1000110110	6.5	25.00000	1.300000	2015	6
1010100110	9.5	19.30000	0.600000	2015	14
1110110010	4.5	24.20000	1.300000	2015	1
1110000101	6.5	27.20000	1.700000	2015	6
1110110000	4.5	24.60000	1.400000	2015	1
1000000000	7.5	33.50000	3.000000	2015	9
1010110100	6.5	23.60000	1.150000	2015	6
1110100000	4.5	23.90000	1.250000	2015	1
1010110000	4.5	24.00000	1.100000	2015	1
1010100001	7.5	32.00000	1.900000	2015	9
1110110010	4.5	24.00000	1.150000	2015	1
1110110000	5.5	25.40000	1.600000	2015	3
1000000000	5.5	28.10000	2.050000	2015	3
0001100010	5.5	27.60000	1.842000	2017	4
1110110110	4.5	25.10000	1.400000	2015	1
1010100100	6.5	23.30000	0.750000	2015	6
1000010111	4.5	23.50000	1.000000	2015	1
1100110111	7.5	28.50000	1.800000	2015	9
1010100100	6.5	30.40000	2.300000	2015	6
1110110100	4.5	24.00000	1.200000	2015	1
1110110110	4.5	24.00000	1.200000	2015	1
0001100010	4.5	27.30000	1.999000	2017	2
0001000000	7.5	24.00000	1.200000	2017	10
0001110101	4.5	25.40000	1.400000	2017	2
0001110100	5.5	28.00000	1.839000	2017	4
0001010000	7.5	23.50000	1.100000	2017	10
0001110110	4.5	25.30000	1.400000	2017	2
0001110010	7.5	25.20000	1.700000	2017	10
0001010110	6.5	27.30000	2.000000	2017	7
0001000110	5.5	23.70000	0.991000	2017	4
0001010111	7.5	22.30000	1.000000	2017	10
0001110111	4.5	24.90000	1.200000	2017	2
0001110111	7.5	24.00000	1.200000	2017	10
0001110001	6.5	27.10000	2.000000	2017	7
0001010110	5.5	24.90000	1.305000	2017	4
0001100001	4.5	24.50000	1.270000	2017	2
0001010101	5.5	24.70000	1.329000	2017	4
0001110111	6.5	26.90000	1.700000	2017	7
0001110110	4.5	24.10000	1.190000	2017	2
0001010100	7.5	25.60000	1.400000	2017	10
0001110101	6.5	24.10000	1.200000	2017	7
0001110110	4.5	25.00000	1.300000	2017	2
0001110111	5.5	26.40000	1.554000	2017	4
0001110111	7.5	24.60000	1.400000	2017	10
0001010011	5.5	23.90000	1.230000	2017	4
0001100110	6.5	24.40000	1.400000	2017	7
0001010100	7.5	26.50000	1.700000	2017	10
0001110110	6.5	27.10000	1.700000	2017	7
0001110110	5.5	26.90000	1.823000	2017	4
0001110101	5.5	24.10000	1.242000	2017	4
0001110111	5.5	25.10000	1.534000	2017	4
0001110111	4.5	26.20000	1.500000	2017	2
0001000101	7.5	25.20000	1.500000	2017	10
0001110011	5.5	27.90000	1.530000	2017	4
1110110000	7.5	33.40000	3.200000	2015	9
0001110111	6.5	25.70000	1.400000	2017	7
0001110110	4.5	24.20000	1.200000	2017	2
0001000111	7.5	29.00000	2.200000	2017	10
0001010011	7.5	30.00000	2.500000	2017	10
0001100001	5.5	26.60000	1.635000	2017	4
0001000110	7.5	28.10000	2.100000	2017	10
0001110111	4.5	26.10000	1.370000	2017	2
0001110111	5.5	24.80000	1.175000	2017	4
0001110110	5.5	29.60000	2.354000	2017	4
0001000000	5.5	25.00000	1.196000	2017	4
0001110010	5.5	24.70000	1.261000	2017	4
0001010101	6.5	28.00000	2.100000	2017	7
0001110010	5.5	26.60000	1.744000	2017	4
0001110110	5.5	26.50000	1.742000	2017	4
0001110100	7.5	26.60000	1.600000	2017	10
0001100010	7.5	27.50000	2.000000	2017	10
0001100001	6.5	26.90000	1.600000	2017	7
0001110000	5.5	24.20000	1.391000	2017	4
0001110000	4.5	25.40000	1.400000	2017	2
0001010100	6.5	27.50000	1.900000	2017	7
0001110110	5.5	26.50000	1.524000	2017	4
0001110110	5.5	24.00000	1.162000	2017	4
0001000000	7.5	28.30000	2.000000	2017	10
0001110011	7.5	23.80000	1.100000	2017	10
0001100110	6.5	27.90000	2.200000	2017	7
0001110111	5.5	26.10000	1.647000	2017	4
0001110111	5.5	25.50000	1.393000	2017	4
0001010111	5.5	24.20000	1.085000	2017	4
0001110011	5.5	25.70000	1.487000	2017	4
0001000110	7.5	27.70000	1.100000	2017	10
0001000000	7.5	24.30000	1.200000	2017	10
0001110111	5.5	25.70000	1.343000	2017	4
0001110110	4.5	25.30000	1.300000	2017	2
0001110111	5.5	23.60000	1.504000	2017	4
0001000000	6.5	27.20000	1.900000	2017	7
0001110000	5.5	24.90000	1.196000	2017	4
0001010110	7.5	26.80000	1.800000	2017	10
0001000000	7.5	27.20000	1.800000	2017	10
0001010111	6.5	28.50000	2.200000	2017	7
0001110110	4.5	24.60000	1.200000	2017	2
0001110111	4.5	24.60000	1.200000	2017	2
0001000111	5.5	25.90000	1.367000	2017	4
0001100000	6.5	26.90000	1.800000	2017	7
0001110001	5.5	25.40000	1.407000	2017	4
0001000000	6.5	26.90000	1.800000	2017	7
0001000010	5.5	24.30000	1.270000	2017	4
0001110011	6.5	26.50000	1.600000	2017	7
1000000010	5.5	26.00000	1.550000	2015	3
0001100010	5.5	27.80000	1.879000	2017	4
0001110101	6.5	27.50000	2.000000	2017	7
0001010111	5.5	25.90000	1.537000	2017	4
0001100110	4.5	24.80000	1.250000	2017	2
0001110000	4.5	25.20000	1.300000	2017	2
0001110111	6.5	27.30000	1.800000	2017	7
0001110111	7.5	26.00000	1.500000	2017	10
0001000000	4.5	26.90000	1.800000	2017	2
0001010010	4.5	25.10000	1.310000	2017	2
0001110111	4.5	26.10000	1.600000	2017	2
0001110011	5.5	27.00000	1.718000	2017	4
0001010110	5.5	24.40000	1.051000	2017	4
0001110010	5.5	26.50000	1.603000	2017	4
0001010100	6.5	27.10000	1.300000	2017	7
0001110010	6.5	27.20000	2.000000	2017	7
0001110110	7.5	25.00000	1.500000	2017	10
0001110110	5.5	26.70000	1.643000	2017	4
0001110110	4.5	25.20000	1.200000	2017	2
0001010110	6.5	27.30000	1.200000	2017	7
0001010000	4.5	23.80000	1.100000	2017	2
0001110111	6.5	27.30000	2.000000	2017	7
0001110110	5.5	23.50000	0.972000	2017	4
0001010000	7.5	26.30000	1.500000	2017	10
0001010110	5.5	26.20000	1.653000	2017	4
0001110000	4.5	25.30000	1.500000	2017	2
0001010010	7.5	29.70000	2.200000	2017	10
0001110101	4.5	24.90000	1.300000	2017	2
0001100010	7.5	24.90000	1.500000	2017	10
0001110110	5.5	26.00000	1.443000	2017	4
0001110111	6.5	26.00000	1.600000	2017	7
0001110000	4.5	25.90000	1.400000	2017	2
0001110100	5.5	24.90000	1.139000	2017	4
0001010110	4.5	24.10000	1.200000	2017	2
0001100000	5.5	26.30000	1.479000	2017	4
0001100110	6.5	27.10000	2.000000	2017	7
0001100000	6.5	29.80000	2.400000	2017	7
0001110110	5.5	25.60000	1.377000	2017	4
0001000001	4.5	26.00000	1.600000	2017	2
0001110110	7.5	25.00000	1.200000	2017	10
0001110111	5.5	25.90000	1.529000	2017	4
0001110101	6.5	26.40000	0.900000	2017	7
0001110101	6.5	25.10000	1.400000	2017	7
0001000111	6.5	28.20000	2.100000	2017	7
0001110111	5.5	30.60000	2.593000	2017	4
0001110010	6.5	28.00000	2.200000	2017	7
0001010111	6.5	26.60000	1.600000	2017	7
0001010100	5.5	26.60000	1.489000	2017	4
0001110111	4.5	25.50000	1.400000	2017	2
0001110101	5.5	25.60000	1.326000	2017	4
0001100111	6.5	24.00000	1.400000	2017	7
0001100000	4.5	25.30000	1.200000	2017	2
0001010100	5.5	26.40000	1.384000	2017	4
0001110110	4.5	26.90000	1.500000	2017	2
0001110010	5.5	25.20000	1.265000	2017	4
0001010100	4.5	25.20000	1.400000	2017	2
0001000110	5.5	25.10000	1.427000	2017	4
0001110110	5.5	23.40000	1.027000	2017	4
0001000111	4.5	24.30000	1.220000	2017	2
0001010001	6.5	28.00000	2.000000	2017	7
0001110111	5.5	24.00000	1.153000	2017	4
0001110111	5.5	27.10000	1.889000	2017	4
0001110001	6.5	26.50000	1.600000	2017	7
0001110110	6.5	24.60000	1.300000	2017	7
0001110000	5.5	25.50000	1.578000	2017	4
0001100110	7.5	25.20000	1.600000	2017	10
0001110111	6.5	31.40000	2.900000	2017	7
0001110110	5.5	26.20000	1.695000	2017	4
0001010101	4.5	26.70000	1.600000	2017	2
0001110100	5.5	23.70000	1.217000	2017	4
0001010111	4.5	25.20000	1.500000	2017	2
0001110111	4.5	25.30000	1.500000	2017	2
0001110000	4.5	26.70000	1.600000	2017	2
0001110001	4.5	23.90000	1.200000	2017	2
0001010000	4.5	25.00000	1.300000	2017	2
0001110111	5.5	24.80000	1.196000	2017	4
0001010111	7.5	27.00000	1.200000	2017	10
0001110010	6.5	25.70000	1.550000	2017	7
0001100101	5.5	28.60000	2.111000	2017	4
0001100110	4.5	24.60000	1.300000	2017	2
0001000000	5.5	25.40000	1.251000	2017	4
0001110111	6.5	26.50000	1.800000	2017	7
0001000000	5.5	24.30000	1.624000	2017	4
0001110101	4.5	24.40000	1.200000	2017	2
0001010111	5.5	25.60000	1.480000	2017	4
0001110111	5.5	26.60000	0.984000	2017	4
0001110011	5.5	26.00000	1.668000	2017	4
0001110001	7.5	25.00000	1.300000	2017	10
0001110110	5.5	26.30000	1.453000	2017	4
0001110000	5.5	26.70000	1.608000	2017	4
0000001111	6.5	29.90000	2.586000	2019	8
0001100001	5.5	27.10000	1.781000	2017	4
0001000111	5.5	26.00000	1.462000	2017	4
0001110100	5.5	27.00000	1.780000	2017	4
0001100110	5.5	25.90000	1.488000	2017	4
0001110100	5.5	25.70000	1.383000	2017	4
0001000011	5.5	26.80000	1.849000	2017	4
0001110100	5.5	28.70000	2.095000	2017	4
0001000100	5.5	24.00000	1.257000	2017	4
0001110011	5.5	25.90000	1.633000	2017	4
0001110000	5.5	29.10000	2.200000	2017	4
0001100110	5.5	28.50000	2.067000	2017	4
0001010110	5.5	26.00000	1.587000	2017	4
0001110000	5.5	26.50000	1.584000	2017	4
0001010110	5.5	24.90000	1.277000	2017	4
0001110100	5.5	26.30000	1.702000	2017	4
1000110110	7.5	22.50000	1.000000	2015	9
0001110100	5.5	26.90000	1.614000	2017	4
0000001111	7.5	28.10000	2.082000	2019	11
0000001111	5.5	26.70000	1.481000	2019	5
0000001110	7.5	28.30000	1.980000	2019	11
0000001010	8.5	29.30000	2.206000	2019	13
0000001100	7.5	25.90000	1.489000	2019	11
0000001100	7.5	25.30000	1.281000	2019	11
0000001001	7.5	25.10000	1.380000	2019	11
0000001100	7.5	24.30000	1.323000	2019	11
0000001100	5.5	28.10000	1.853000	2019	5
0000001111	7.5	25.60000	1.442000	2019	11
0000001110	5.5	27.90000	1.682000	2019	5
0000001110	5.5	27.40000	1.641000	2019	5
0000001111	5.5	29.90000	2.226000	2019	5
0000001110	8.5	27.30000	1.602000	2019	13
0000001110	8.5	28.50000	2.129000	2019	13
0000001110	7.5	27.10000	1.676000	2019	11
0000001110	7.5	27.50000	1.637000	2019	11
0000001110	6.5	28.70000	2.038000	2019	8
0000001010	5.5	29.80000	2.753000	2019	5
0000001100	6.5	29.80000	2.314000	2019	8
0000001111	6.5	28.90000	2.392000	2019	8
0000001100	8.5	27.50000	1.636000	2019	13
0000001000	6.5	29.10000	2.231000	2019	8
0000001111	5.5	31.20000	2.388000	2019	5
0000001110	5.5	28.30000	1.888000	2019	5
0000001111	6.5	29.30000	2.144000	2019	8
0000001111	8.5	29.50000	2.218000	2019	13
0000001110	5.5	24.40000	1.134000	2019	5
0000001000	5.5	28.60000	1.976000	2019	5
0000001100	5.5	25.90000	1.592000	2019	5
0000001110	7.5	28.40000	2.806000	2019	11
0000001100	7.5	27.50000	1.672000	2019	11
0000001001	7.5	24.20000	1.239000	2019	11
0000001110	7.5	27.20000	1.715000	2019	11
0000001101	6.5	29.30000	2.243000	2019	8
0000001111	6.5	31.10000	2.870000	2019	8
0000001110	6.5	30.10000	2.537000	2019	8
0000001010	5.5	29.70000	1.894000	2019	5
0000001011	5.5	28.20000	1.810000	2019	5
0000001110	6.5	30.70000	2.545000	2019	8
0000001100	5.5	25.80000	1.527000	2019	5
0000001100	7.5	27.70000	1.866000	2019	11
0000001101	6.5	27.60000	1.997000	2019	8
0000001111	8.5	25.30000	1.328000	2019	13
0000001110	6.5	27.50000	1.835000	2019	8
0000001111	6.5	27.70112	1.884132	2019	8
0000001110	5.5	26.90000	1.614000	2019	5
0000001010	6.5	29.10000	2.299000	2019	8
0000001110	6.5	31.70000	2.955000	2019	8
0000001110	5.5	28.20000	1.808000	2019	5
0000001110	5.5	26.30000	1.473000	2019	5
0000001101	5.5	25.90000	1.257000	2019	5
0000001100	6.5	27.90000	1.661000	2019	8
0000001111	6.5	30.20000	2.591000	2019	8
0000001100	7.5	26.50000	1.800000	2019	11
0000001110	6.5	28.20000	1.829000	2019	8
0000001100	6.5	29.50000	2.309000	2019	8
0000001100	5.5	28.80000	1.832000	2019	5
0000001111	6.5	28.60000	2.221000	2019	8
0000001110	5.5	27.50000	1.654000	2019	5
0000001011	5.5	30.80000	2.328000	2019	5
0000001100	5.5	26.60000	1.714000	2019	5
0000001110	5.5	27.00000	1.537000	2019	5
0000001111	5.5	26.50000	1.480000	2019	5
0000001110	6.5	30.90000	2.768000	2019	8
0000001010	6.5	29.50000	2.227000	2019	8
0000001110	6.5	23.30000	1.043000	2019	8
0000001010	6.5	27.50000	1.864000	2019	8
0000001111	5.5	28.10000	2.003000	2019	5
0000001110	5.5	30.20000	2.399000	2019	5
0000001100	7.5	25.80000	1.466000	2019	11
0000001011	8.5	26.10000	1.498000	2019	13
0000001000	5.5	29.20000	2.097000	2019	5
0000001110	8.5	23.40000	1.089000	2019	13
0000001110	6.5	31.30000	3.006000	2019	8
0000001100	5.5	27.20000	1.694000	2019	5
0000001110	5.5	26.60000	1.331000	2019	5
0000001111	6.5	29.30000	2.182000	2019	8
0000001111	5.5	28.40000	1.941000	2019	5
0000001110	5.5	27.90000	1.793000	2019	5
0000001111	5.5	27.60000	1.709000	2019	5
0000001100	5.5	25.40000	1.266000	2019	5
0000001101	6.5	29.70000	2.366000	2019	8
0000001101	5.5	29.20000	2.186000	2019	5
0000001000	5.5	26.80000	1.518000	2019	5
0000001110	5.5	26.40000	1.494000	2019	5
0000001100	5.5	25.70000	1.520000	2019	5
0000001110	5.5	26.60000	1.729000	2019	5
0000001111	5.5	28.40000	1.872000	2019	5
0000001101	5.5	31.10000	2.588000	2019	5
0000001011	6.5	30.10000	2.624000	2019	8
0000001111	5.5	26.20000	2.053000	2019	5
0000001111	6.5	26.50000	1.762000	2019	8
0000001111	5.5	30.40000	2.400000	2019	5
0000001111	6.5	28.90000	2.002000	2019	8
0000001110	6.5	27.50000	2.088000	2019	8
0000001000	5.5	28.70000	2.017000	2019	5
0000001010	6.5	30.10000	2.502000	2019	8
0000001110	5.5	25.50000	1.216000	2019	5
0000001110	5.5	29.10000	1.967000	2019	5
0000001101	5.5	25.90000	1.455000	2019	5
0000001010	5.5	31.20000	2.707000	2019	5
0000001101	5.5	26.40000	1.561000	2019	5
0000001100	5.5	30.50000	2.442000	2019	5
0000001010	5.5	28.80000	1.741000	2019	5
0000001101	5.5	26.30000	1.672000	2019	5
0000001110	6.5	29.80000	2.298000	2019	8
0000001101	5.5	28.20000	1.707000	2019	5
0000001110	5.5	25.80000	1.432000	2019	5
0000001101	6.5	30.70000	2.724000	2019	8
0000001111	6.5	27.80000	1.979000	2019	8
0000001110	5.5	26.20000	1.432000	2019	5
0000001110	5.5	25.60000	1.334000	2019	5
0000001111	6.5	26.60000	1.602000	2019	8
0000001111	5.5	27.10000	1.476000	2019	5
0000001110	5.5	26.70000	1.473000	2019	5
0000001000	6.5	25.30000	1.342000	2019	8
0000001011	6.5	28.30000	2.055000	2019	8
0000001111	5.5	27.60000	1.769000	2019	5
0000001101	6.5	26.70000	1.739000	2019	8
0000001100	5.5	25.50000	1.257000	2019	5
0000001111	6.5	27.80000	1.982000	2019	8
0000001110	5.5	25.60000	1.371000	2019	5
0000001101	6.5	28.50000	2.138000	2019	8
0000001100	5.5	28.10000	1.675000	2019	5
0000001110	5.5	26.80000	1.649000	2019	5
0000001110	5.5	29.50000	2.209000	2019	5
0000001101	5.5	25.30000	1.251000	2019	5
0000001110	6.5	29.80000	2.289000	2019	8
0000001101	5.5	25.90000	1.543000	2019	5
0000001100	5.5	27.90000	1.673000	2019	5
0000001111	5.5	29.90000	2.180000	2019	5
0000001110	6.5	26.60000	1.668000	2019	8
0000001101	5.5	27.40000	1.996000	2019	5
0000001110	5.5	29.30000	2.033000	2019	5
0000001000	5.5	27.30000	1.602000	2019	5
0000001101	5.5	27.30000	1.693000	2019	5
0000001110	5.5	27.50000	1.805000	2019	5
0000001110	5.5	27.90000	1.966000	2019	5
0000001110	5.5	24.70000	1.203000	2019	5
0000001000	5.5	25.30000	1.325000	2019	5
0000001110	5.5	29.90000	2.265000	2019	5
0000001100	5.5	25.50000	1.396000	2019	5
0000001110	6.5	29.20000	2.203000	2019	8
0000001010	5.5	24.80000	1.237000	2019	5
0000001100	5.5	29.20000	2.046000	2019	5
0000001010	5.5	29.60000	2.160000	2019	5
0000001111	5.5	25.10000	1.293000	2019	5
0000001110	5.5	27.90000	1.865000	2019	5
0000001010	6.5	26.30000	1.739000	2019	8
0000001111	5.5	28.80000	2.071000	2019	5
0000001110	5.5	29.90000	2.206000	2019	5
0000001111	5.5	28.50000	1.921000	2019	5
0000001001	6.5	27.40000	1.829000	2019	8

Now we’ll make the design data for CJS. We have to fix two parameters–detection for the 2015 cohort of tortoises in April of 2017 and detection for the 2015 and 2017 cohorts in February of 2019. The new cohorts of tortoises were released then, but no surveys were conducted. So we need MARK to know that detection for the older cohorts in those time periods was zero.

# make CJS ddl
tortoises.ddl <- make.design.data(tortoises.process)

# merge effort data
tortoises.ddl$p <- merge_design.covariates(tortoises.ddl$p,effortcov, bytime = TRUE)

# fix detection for the 2015 cohort in occasion 4 (time 1.83) when no sampling occured
tortoises.ddl$p$fix <- NA
tortoises.ddl$p$fix[tortoises.ddl$p$time == "1.83" & 
                      tortoises.ddl$p$release_cohort == "2015"] <- 0

# fix detection for the 2015 & 2017 cohorts in occassion 7 (time 3.67) when no sampling occured
tortoises.ddl$p$fix[tortoises.ddl$p$time == "3.67" &
                      c(tortoises.ddl$p$release_cohort == "2015" |
                          tortoises.ddl$p$release_cohort == "2017")] <- 0

# design data PIMS
kable(tortoises.ddl[[1]][], "html", 
      caption = "PIMS for Phi (survival) parameter") %>% 
  kable_styling(bootstrap_options = c("striped", "condensed")) %>%
  scroll_box(height = "300px")

PIMS for Phi (survival) parameter

par.index	model.index	group	cohort	age	time	occ.cohort	Cohort	Age	Time	release_cohort	age_release
1	1	20154.5	0	4.5	0	1	0.00	4.50	0.00	2015	4.5
2	2	20154.5	0	4.67	0.17	1	0.00	4.67	0.17	2015	4.5
3	3	20154.5	0	5.5	1	1	0.00	5.50	1.00	2015	4.5
4	4	20154.5	0	6.33	1.83	1	0.00	6.33	1.83	2015	4.5
5	5	20154.5	0	6.5	2	1	0.00	6.50	2.00	2015	4.5
6	6	20154.5	0	7.5	3	1	0.00	7.50	3.00	2015	4.5
7	7	20154.5	0	8.17	3.67	1	0.00	8.17	3.67	2015	4.5
8	8	20154.5	0	8.34	3.84	1	0.00	8.34	3.84	2015	4.5
9	9	20154.5	0	8.67	4.17	1	0.00	8.67	4.17	2015	4.5
10	10	20154.5	0.17	4.5	0.17	2	0.17	4.50	0.17	2015	4.5
11	11	20154.5	0.17	5.33	1	2	0.17	5.33	1.00	2015	4.5
12	12	20154.5	0.17	6.16	1.83	2	0.17	6.16	1.83	2015	4.5
13	13	20154.5	0.17	6.33	2	2	0.17	6.33	2.00	2015	4.5
14	14	20154.5	0.17	7.33	3	2	0.17	7.33	3.00	2015	4.5
15	15	20154.5	0.17	8	3.67	2	0.17	8.00	3.67	2015	4.5
16	16	20154.5	0.17	8.17	3.84	2	0.17	8.17	3.84	2015	4.5
17	17	20154.5	0.17	8.5	4.17	2	0.17	8.50	4.17	2015	4.5
18	18	20154.5	1	4.5	1	3	1.00	4.50	1.00	2015	4.5
19	19	20154.5	1	5.33	1.83	3	1.00	5.33	1.83	2015	4.5
20	20	20154.5	1	5.5	2	3	1.00	5.50	2.00	2015	4.5
21	21	20154.5	1	6.5	3	3	1.00	6.50	3.00	2015	4.5
22	22	20154.5	1	7.17	3.67	3	1.00	7.17	3.67	2015	4.5
23	23	20154.5	1	7.34	3.84	3	1.00	7.34	3.84	2015	4.5
24	24	20154.5	1	7.67	4.17	3	1.00	7.67	4.17	2015	4.5
25	25	20154.5	1.83	4.5	1.83	4	1.83	4.50	1.83	2015	4.5
26	26	20154.5	1.83	4.67	2	4	1.83	4.67	2.00	2015	4.5
27	27	20154.5	1.83	5.67	3	4	1.83	5.67	3.00	2015	4.5
28	28	20154.5	1.83	6.34	3.67	4	1.83	6.34	3.67	2015	4.5
29	29	20154.5	1.83	6.51	3.84	4	1.83	6.51	3.84	2015	4.5
30	30	20154.5	1.83	6.84	4.17	4	1.83	6.84	4.17	2015	4.5
31	31	20154.5	2	4.5	2	5	2.00	4.50	2.00	2015	4.5
32	32	20154.5	2	5.5	3	5	2.00	5.50	3.00	2015	4.5
33	33	20154.5	2	6.17	3.67	5	2.00	6.17	3.67	2015	4.5
34	34	20154.5	2	6.34	3.84	5	2.00	6.34	3.84	2015	4.5
35	35	20154.5	2	6.67	4.17	5	2.00	6.67	4.17	2015	4.5
36	36	20154.5	3	4.5	3	6	3.00	4.50	3.00	2015	4.5
37	37	20154.5	3	5.17	3.67	6	3.00	5.17	3.67	2015	4.5
38	38	20154.5	3	5.34	3.84	6	3.00	5.34	3.84	2015	4.5
39	39	20154.5	3	5.67	4.17	6	3.00	5.67	4.17	2015	4.5
40	40	20154.5	3.67	4.5	3.67	7	3.67	4.50	3.67	2015	4.5
41	41	20154.5	3.67	4.67	3.84	7	3.67	4.67	3.84	2015	4.5
42	42	20154.5	3.67	5	4.17	7	3.67	5.00	4.17	2015	4.5
43	43	20154.5	3.84	4.5	3.84	8	3.84	4.50	3.84	2015	4.5
44	44	20154.5	3.84	4.83	4.17	8	3.84	4.83	4.17	2015	4.5
45	45	20154.5	4.17	4.5	4.17	9	4.17	4.50	4.17	2015	4.5
46	46	20174.5	0	4.5	0	1	0.00	4.50	0.00	2017	4.5
47	47	20174.5	0	4.67	0.17	1	0.00	4.67	0.17	2017	4.5
48	48	20174.5	0	5.5	1	1	0.00	5.50	1.00	2017	4.5
49	49	20174.5	0	6.33	1.83	1	0.00	6.33	1.83	2017	4.5
50	50	20174.5	0	6.5	2	1	0.00	6.50	2.00	2017	4.5
51	51	20174.5	0	7.5	3	1	0.00	7.50	3.00	2017	4.5
52	52	20174.5	0	8.17	3.67	1	0.00	8.17	3.67	2017	4.5
53	53	20174.5	0	8.34	3.84	1	0.00	8.34	3.84	2017	4.5
54	54	20174.5	0	8.67	4.17	1	0.00	8.67	4.17	2017	4.5
55	55	20174.5	0.17	4.5	0.17	2	0.17	4.50	0.17	2017	4.5
56	56	20174.5	0.17	5.33	1	2	0.17	5.33	1.00	2017	4.5
57	57	20174.5	0.17	6.16	1.83	2	0.17	6.16	1.83	2017	4.5
58	58	20174.5	0.17	6.33	2	2	0.17	6.33	2.00	2017	4.5
59	59	20174.5	0.17	7.33	3	2	0.17	7.33	3.00	2017	4.5
60	60	20174.5	0.17	8	3.67	2	0.17	8.00	3.67	2017	4.5
61	61	20174.5	0.17	8.17	3.84	2	0.17	8.17	3.84	2017	4.5
62	62	20174.5	0.17	8.5	4.17	2	0.17	8.50	4.17	2017	4.5
63	63	20174.5	1	4.5	1	3	1.00	4.50	1.00	2017	4.5
64	64	20174.5	1	5.33	1.83	3	1.00	5.33	1.83	2017	4.5
65	65	20174.5	1	5.5	2	3	1.00	5.50	2.00	2017	4.5
66	66	20174.5	1	6.5	3	3	1.00	6.50	3.00	2017	4.5
67	67	20174.5	1	7.17	3.67	3	1.00	7.17	3.67	2017	4.5
68	68	20174.5	1	7.34	3.84	3	1.00	7.34	3.84	2017	4.5
69	69	20174.5	1	7.67	4.17	3	1.00	7.67	4.17	2017	4.5
70	70	20174.5	1.83	4.5	1.83	4	1.83	4.50	1.83	2017	4.5
71	71	20174.5	1.83	4.67	2	4	1.83	4.67	2.00	2017	4.5
72	72	20174.5	1.83	5.67	3	4	1.83	5.67	3.00	2017	4.5
73	73	20174.5	1.83	6.34	3.67	4	1.83	6.34	3.67	2017	4.5
74	74	20174.5	1.83	6.51	3.84	4	1.83	6.51	3.84	2017	4.5
75	75	20174.5	1.83	6.84	4.17	4	1.83	6.84	4.17	2017	4.5
76	76	20174.5	2	4.5	2	5	2.00	4.50	2.00	2017	4.5
77	77	20174.5	2	5.5	3	5	2.00	5.50	3.00	2017	4.5
78	78	20174.5	2	6.17	3.67	5	2.00	6.17	3.67	2017	4.5
79	79	20174.5	2	6.34	3.84	5	2.00	6.34	3.84	2017	4.5
80	80	20174.5	2	6.67	4.17	5	2.00	6.67	4.17	2017	4.5
81	81	20174.5	3	4.5	3	6	3.00	4.50	3.00	2017	4.5
82	82	20174.5	3	5.17	3.67	6	3.00	5.17	3.67	2017	4.5
83	83	20174.5	3	5.34	3.84	6	3.00	5.34	3.84	2017	4.5
84	84	20174.5	3	5.67	4.17	6	3.00	5.67	4.17	2017	4.5
85	85	20174.5	3.67	4.5	3.67	7	3.67	4.50	3.67	2017	4.5
86	86	20174.5	3.67	4.67	3.84	7	3.67	4.67	3.84	2017	4.5
87	87	20174.5	3.67	5	4.17	7	3.67	5.00	4.17	2017	4.5
88	88	20174.5	3.84	4.5	3.84	8	3.84	4.50	3.84	2017	4.5
89	89	20174.5	3.84	4.83	4.17	8	3.84	4.83	4.17	2017	4.5
90	90	20174.5	4.17	4.5	4.17	9	4.17	4.50	4.17	2017	4.5
91	91	20155.5	0	5.5	0	1	0.00	5.50	0.00	2015	5.5
92	92	20155.5	0	5.67	0.17	1	0.00	5.67	0.17	2015	5.5
93	93	20155.5	0	6.5	1	1	0.00	6.50	1.00	2015	5.5
94	94	20155.5	0	7.33	1.83	1	0.00	7.33	1.83	2015	5.5
95	95	20155.5	0	7.5	2	1	0.00	7.50	2.00	2015	5.5
96	96	20155.5	0	8.5	3	1	0.00	8.50	3.00	2015	5.5
97	97	20155.5	0	9.17	3.67	1	0.00	9.17	3.67	2015	5.5
98	98	20155.5	0	9.34	3.84	1	0.00	9.34	3.84	2015	5.5
99	99	20155.5	0	9.67	4.17	1	0.00	9.67	4.17	2015	5.5
100	100	20155.5	0.17	5.5	0.17	2	0.17	5.50	0.17	2015	5.5
101	101	20155.5	0.17	6.33	1	2	0.17	6.33	1.00	2015	5.5
102	102	20155.5	0.17	7.16	1.83	2	0.17	7.16	1.83	2015	5.5
103	103	20155.5	0.17	7.33	2	2	0.17	7.33	2.00	2015	5.5
104	104	20155.5	0.17	8.33	3	2	0.17	8.33	3.00	2015	5.5
105	105	20155.5	0.17	9	3.67	2	0.17	9.00	3.67	2015	5.5
106	106	20155.5	0.17	9.17	3.84	2	0.17	9.17	3.84	2015	5.5
107	107	20155.5	0.17	9.5	4.17	2	0.17	9.50	4.17	2015	5.5
108	108	20155.5	1	5.5	1	3	1.00	5.50	1.00	2015	5.5
109	109	20155.5	1	6.33	1.83	3	1.00	6.33	1.83	2015	5.5
110	110	20155.5	1	6.5	2	3	1.00	6.50	2.00	2015	5.5
111	111	20155.5	1	7.5	3	3	1.00	7.50	3.00	2015	5.5
112	112	20155.5	1	8.17	3.67	3	1.00	8.17	3.67	2015	5.5
113	113	20155.5	1	8.34	3.84	3	1.00	8.34	3.84	2015	5.5
114	114	20155.5	1	8.67	4.17	3	1.00	8.67	4.17	2015	5.5
115	115	20155.5	1.83	5.5	1.83	4	1.83	5.50	1.83	2015	5.5
116	116	20155.5	1.83	5.67	2	4	1.83	5.67	2.00	2015	5.5
117	117	20155.5	1.83	6.67	3	4	1.83	6.67	3.00	2015	5.5
118	118	20155.5	1.83	7.34	3.67	4	1.83	7.34	3.67	2015	5.5
119	119	20155.5	1.83	7.51	3.84	4	1.83	7.51	3.84	2015	5.5
120	120	20155.5	1.83	7.84	4.17	4	1.83	7.84	4.17	2015	5.5
121	121	20155.5	2	5.5	2	5	2.00	5.50	2.00	2015	5.5
122	122	20155.5	2	6.5	3	5	2.00	6.50	3.00	2015	5.5
123	123	20155.5	2	7.17	3.67	5	2.00	7.17	3.67	2015	5.5
124	124	20155.5	2	7.34	3.84	5	2.00	7.34	3.84	2015	5.5
125	125	20155.5	2	7.67	4.17	5	2.00	7.67	4.17	2015	5.5
126	126	20155.5	3	5.5	3	6	3.00	5.50	3.00	2015	5.5
127	127	20155.5	3	6.17	3.67	6	3.00	6.17	3.67	2015	5.5
128	128	20155.5	3	6.34	3.84	6	3.00	6.34	3.84	2015	5.5
129	129	20155.5	3	6.67	4.17	6	3.00	6.67	4.17	2015	5.5
130	130	20155.5	3.67	5.5	3.67	7	3.67	5.50	3.67	2015	5.5
131	131	20155.5	3.67	5.67	3.84	7	3.67	5.67	3.84	2015	5.5
132	132	20155.5	3.67	6	4.17	7	3.67	6.00	4.17	2015	5.5
133	133	20155.5	3.84	5.5	3.84	8	3.84	5.50	3.84	2015	5.5
134	134	20155.5	3.84	5.83	4.17	8	3.84	5.83	4.17	2015	5.5
135	135	20155.5	4.17	5.5	4.17	9	4.17	5.50	4.17	2015	5.5
136	136	20175.5	0	5.5	0	1	0.00	5.50	0.00	2017	5.5
137	137	20175.5	0	5.67	0.17	1	0.00	5.67	0.17	2017	5.5
138	138	20175.5	0	6.5	1	1	0.00	6.50	1.00	2017	5.5
139	139	20175.5	0	7.33	1.83	1	0.00	7.33	1.83	2017	5.5
140	140	20175.5	0	7.5	2	1	0.00	7.50	2.00	2017	5.5
141	141	20175.5	0	8.5	3	1	0.00	8.50	3.00	2017	5.5
142	142	20175.5	0	9.17	3.67	1	0.00	9.17	3.67	2017	5.5
143	143	20175.5	0	9.34	3.84	1	0.00	9.34	3.84	2017	5.5
144	144	20175.5	0	9.67	4.17	1	0.00	9.67	4.17	2017	5.5
145	145	20175.5	0.17	5.5	0.17	2	0.17	5.50	0.17	2017	5.5
146	146	20175.5	0.17	6.33	1	2	0.17	6.33	1.00	2017	5.5
147	147	20175.5	0.17	7.16	1.83	2	0.17	7.16	1.83	2017	5.5
148	148	20175.5	0.17	7.33	2	2	0.17	7.33	2.00	2017	5.5
149	149	20175.5	0.17	8.33	3	2	0.17	8.33	3.00	2017	5.5
150	150	20175.5	0.17	9	3.67	2	0.17	9.00	3.67	2017	5.5
151	151	20175.5	0.17	9.17	3.84	2	0.17	9.17	3.84	2017	5.5
152	152	20175.5	0.17	9.5	4.17	2	0.17	9.50	4.17	2017	5.5
153	153	20175.5	1	5.5	1	3	1.00	5.50	1.00	2017	5.5
154	154	20175.5	1	6.33	1.83	3	1.00	6.33	1.83	2017	5.5
155	155	20175.5	1	6.5	2	3	1.00	6.50	2.00	2017	5.5
156	156	20175.5	1	7.5	3	3	1.00	7.50	3.00	2017	5.5
157	157	20175.5	1	8.17	3.67	3	1.00	8.17	3.67	2017	5.5
158	158	20175.5	1	8.34	3.84	3	1.00	8.34	3.84	2017	5.5
159	159	20175.5	1	8.67	4.17	3	1.00	8.67	4.17	2017	5.5
160	160	20175.5	1.83	5.5	1.83	4	1.83	5.50	1.83	2017	5.5
161	161	20175.5	1.83	5.67	2	4	1.83	5.67	2.00	2017	5.5
162	162	20175.5	1.83	6.67	3	4	1.83	6.67	3.00	2017	5.5
163	163	20175.5	1.83	7.34	3.67	4	1.83	7.34	3.67	2017	5.5
164	164	20175.5	1.83	7.51	3.84	4	1.83	7.51	3.84	2017	5.5
165	165	20175.5	1.83	7.84	4.17	4	1.83	7.84	4.17	2017	5.5
166	166	20175.5	2	5.5	2	5	2.00	5.50	2.00	2017	5.5
167	167	20175.5	2	6.5	3	5	2.00	6.50	3.00	2017	5.5
168	168	20175.5	2	7.17	3.67	5	2.00	7.17	3.67	2017	5.5
169	169	20175.5	2	7.34	3.84	5	2.00	7.34	3.84	2017	5.5
170	170	20175.5	2	7.67	4.17	5	2.00	7.67	4.17	2017	5.5
171	171	20175.5	3	5.5	3	6	3.00	5.50	3.00	2017	5.5
172	172	20175.5	3	6.17	3.67	6	3.00	6.17	3.67	2017	5.5
173	173	20175.5	3	6.34	3.84	6	3.00	6.34	3.84	2017	5.5
174	174	20175.5	3	6.67	4.17	6	3.00	6.67	4.17	2017	5.5
175	175	20175.5	3.67	5.5	3.67	7	3.67	5.50	3.67	2017	5.5
176	176	20175.5	3.67	5.67	3.84	7	3.67	5.67	3.84	2017	5.5
177	177	20175.5	3.67	6	4.17	7	3.67	6.00	4.17	2017	5.5
178	178	20175.5	3.84	5.5	3.84	8	3.84	5.50	3.84	2017	5.5
179	179	20175.5	3.84	5.83	4.17	8	3.84	5.83	4.17	2017	5.5
180	180	20175.5	4.17	5.5	4.17	9	4.17	5.50	4.17	2017	5.5
181	181	20195.5	0	5.5	0	1	0.00	5.50	0.00	2019	5.5
182	182	20195.5	0	5.67	0.17	1	0.00	5.67	0.17	2019	5.5
183	183	20195.5	0	6.5	1	1	0.00	6.50	1.00	2019	5.5
184	184	20195.5	0	7.33	1.83	1	0.00	7.33	1.83	2019	5.5
185	185	20195.5	0	7.5	2	1	0.00	7.50	2.00	2019	5.5
186	186	20195.5	0	8.5	3	1	0.00	8.50	3.00	2019	5.5
187	187	20195.5	0	9.17	3.67	1	0.00	9.17	3.67	2019	5.5
188	188	20195.5	0	9.34	3.84	1	0.00	9.34	3.84	2019	5.5
189	189	20195.5	0	9.67	4.17	1	0.00	9.67	4.17	2019	5.5
190	190	20195.5	0.17	5.5	0.17	2	0.17	5.50	0.17	2019	5.5
191	191	20195.5	0.17	6.33	1	2	0.17	6.33	1.00	2019	5.5
192	192	20195.5	0.17	7.16	1.83	2	0.17	7.16	1.83	2019	5.5
193	193	20195.5	0.17	7.33	2	2	0.17	7.33	2.00	2019	5.5
194	194	20195.5	0.17	8.33	3	2	0.17	8.33	3.00	2019	5.5
195	195	20195.5	0.17	9	3.67	2	0.17	9.00	3.67	2019	5.5
196	196	20195.5	0.17	9.17	3.84	2	0.17	9.17	3.84	2019	5.5
197	197	20195.5	0.17	9.5	4.17	2	0.17	9.50	4.17	2019	5.5
198	198	20195.5	1	5.5	1	3	1.00	5.50	1.00	2019	5.5
199	199	20195.5	1	6.33	1.83	3	1.00	6.33	1.83	2019	5.5
200	200	20195.5	1	6.5	2	3	1.00	6.50	2.00	2019	5.5
201	201	20195.5	1	7.5	3	3	1.00	7.50	3.00	2019	5.5
202	202	20195.5	1	8.17	3.67	3	1.00	8.17	3.67	2019	5.5
203	203	20195.5	1	8.34	3.84	3	1.00	8.34	3.84	2019	5.5
204	204	20195.5	1	8.67	4.17	3	1.00	8.67	4.17	2019	5.5
205	205	20195.5	1.83	5.5	1.83	4	1.83	5.50	1.83	2019	5.5
206	206	20195.5	1.83	5.67	2	4	1.83	5.67	2.00	2019	5.5
207	207	20195.5	1.83	6.67	3	4	1.83	6.67	3.00	2019	5.5
208	208	20195.5	1.83	7.34	3.67	4	1.83	7.34	3.67	2019	5.5
209	209	20195.5	1.83	7.51	3.84	4	1.83	7.51	3.84	2019	5.5
210	210	20195.5	1.83	7.84	4.17	4	1.83	7.84	4.17	2019	5.5
211	211	20195.5	2	5.5	2	5	2.00	5.50	2.00	2019	5.5
212	212	20195.5	2	6.5	3	5	2.00	6.50	3.00	2019	5.5
213	213	20195.5	2	7.17	3.67	5	2.00	7.17	3.67	2019	5.5
214	214	20195.5	2	7.34	3.84	5	2.00	7.34	3.84	2019	5.5
215	215	20195.5	2	7.67	4.17	5	2.00	7.67	4.17	2019	5.5
216	216	20195.5	3	5.5	3	6	3.00	5.50	3.00	2019	5.5
217	217	20195.5	3	6.17	3.67	6	3.00	6.17	3.67	2019	5.5
218	218	20195.5	3	6.34	3.84	6	3.00	6.34	3.84	2019	5.5
219	219	20195.5	3	6.67	4.17	6	3.00	6.67	4.17	2019	5.5
220	220	20195.5	3.67	5.5	3.67	7	3.67	5.50	3.67	2019	5.5
221	221	20195.5	3.67	5.67	3.84	7	3.67	5.67	3.84	2019	5.5
222	222	20195.5	3.67	6	4.17	7	3.67	6.00	4.17	2019	5.5
223	223	20195.5	3.84	5.5	3.84	8	3.84	5.50	3.84	2019	5.5
224	224	20195.5	3.84	5.83	4.17	8	3.84	5.83	4.17	2019	5.5
225	225	20195.5	4.17	5.5	4.17	9	4.17	5.50	4.17	2019	5.5
226	226	20156.5	0	6.5	0	1	0.00	6.50	0.00	2015	6.5
227	227	20156.5	0	6.67	0.17	1	0.00	6.67	0.17	2015	6.5
228	228	20156.5	0	7.5	1	1	0.00	7.50	1.00	2015	6.5
229	229	20156.5	0	8.33	1.83	1	0.00	8.33	1.83	2015	6.5
230	230	20156.5	0	8.5	2	1	0.00	8.50	2.00	2015	6.5
231	231	20156.5	0	9.5	3	1	0.00	9.50	3.00	2015	6.5
232	232	20156.5	0	10.17	3.67	1	0.00	10.17	3.67	2015	6.5
233	233	20156.5	0	10.34	3.84	1	0.00	10.34	3.84	2015	6.5
234	234	20156.5	0	10.67	4.17	1	0.00	10.67	4.17	2015	6.5
235	235	20156.5	0.17	6.5	0.17	2	0.17	6.50	0.17	2015	6.5
236	236	20156.5	0.17	7.33	1	2	0.17	7.33	1.00	2015	6.5
237	237	20156.5	0.17	8.16	1.83	2	0.17	8.16	1.83	2015	6.5
238	238	20156.5	0.17	8.33	2	2	0.17	8.33	2.00	2015	6.5
239	239	20156.5	0.17	9.33	3	2	0.17	9.33	3.00	2015	6.5
240	240	20156.5	0.17	10	3.67	2	0.17	10.00	3.67	2015	6.5
241	241	20156.5	0.17	10.17	3.84	2	0.17	10.17	3.84	2015	6.5
242	242	20156.5	0.17	10.5	4.17	2	0.17	10.50	4.17	2015	6.5
243	243	20156.5	1	6.5	1	3	1.00	6.50	1.00	2015	6.5
244	244	20156.5	1	7.33	1.83	3	1.00	7.33	1.83	2015	6.5
245	245	20156.5	1	7.5	2	3	1.00	7.50	2.00	2015	6.5
246	246	20156.5	1	8.5	3	3	1.00	8.50	3.00	2015	6.5
247	247	20156.5	1	9.17	3.67	3	1.00	9.17	3.67	2015	6.5
248	248	20156.5	1	9.34	3.84	3	1.00	9.34	3.84	2015	6.5
249	249	20156.5	1	9.67	4.17	3	1.00	9.67	4.17	2015	6.5
250	250	20156.5	1.83	6.5	1.83	4	1.83	6.50	1.83	2015	6.5
251	251	20156.5	1.83	6.67	2	4	1.83	6.67	2.00	2015	6.5
252	252	20156.5	1.83	7.67	3	4	1.83	7.67	3.00	2015	6.5
253	253	20156.5	1.83	8.34	3.67	4	1.83	8.34	3.67	2015	6.5
254	254	20156.5	1.83	8.51	3.84	4	1.83	8.51	3.84	2015	6.5
255	255	20156.5	1.83	8.84	4.17	4	1.83	8.84	4.17	2015	6.5
256	256	20156.5	2	6.5	2	5	2.00	6.50	2.00	2015	6.5
257	257	20156.5	2	7.5	3	5	2.00	7.50	3.00	2015	6.5
258	258	20156.5	2	8.17	3.67	5	2.00	8.17	3.67	2015	6.5
259	259	20156.5	2	8.34	3.84	5	2.00	8.34	3.84	2015	6.5
260	260	20156.5	2	8.67	4.17	5	2.00	8.67	4.17	2015	6.5
261	261	20156.5	3	6.5	3	6	3.00	6.50	3.00	2015	6.5
262	262	20156.5	3	7.17	3.67	6	3.00	7.17	3.67	2015	6.5
263	263	20156.5	3	7.34	3.84	6	3.00	7.34	3.84	2015	6.5
264	264	20156.5	3	7.67	4.17	6	3.00	7.67	4.17	2015	6.5
265	265	20156.5	3.67	6.5	3.67	7	3.67	6.50	3.67	2015	6.5
266	266	20156.5	3.67	6.67	3.84	7	3.67	6.67	3.84	2015	6.5
267	267	20156.5	3.67	7	4.17	7	3.67	7.00	4.17	2015	6.5
268	268	20156.5	3.84	6.5	3.84	8	3.84	6.50	3.84	2015	6.5
269	269	20156.5	3.84	6.83	4.17	8	3.84	6.83	4.17	2015	6.5
270	270	20156.5	4.17	6.5	4.17	9	4.17	6.50	4.17	2015	6.5
271	271	20176.5	0	6.5	0	1	0.00	6.50	0.00	2017	6.5
272	272	20176.5	0	6.67	0.17	1	0.00	6.67	0.17	2017	6.5
273	273	20176.5	0	7.5	1	1	0.00	7.50	1.00	2017	6.5
274	274	20176.5	0	8.33	1.83	1	0.00	8.33	1.83	2017	6.5
275	275	20176.5	0	8.5	2	1	0.00	8.50	2.00	2017	6.5
276	276	20176.5	0	9.5	3	1	0.00	9.50	3.00	2017	6.5
277	277	20176.5	0	10.17	3.67	1	0.00	10.17	3.67	2017	6.5
278	278	20176.5	0	10.34	3.84	1	0.00	10.34	3.84	2017	6.5
279	279	20176.5	0	10.67	4.17	1	0.00	10.67	4.17	2017	6.5
280	280	20176.5	0.17	6.5	0.17	2	0.17	6.50	0.17	2017	6.5
281	281	20176.5	0.17	7.33	1	2	0.17	7.33	1.00	2017	6.5
282	282	20176.5	0.17	8.16	1.83	2	0.17	8.16	1.83	2017	6.5
283	283	20176.5	0.17	8.33	2	2	0.17	8.33	2.00	2017	6.5
284	284	20176.5	0.17	9.33	3	2	0.17	9.33	3.00	2017	6.5
285	285	20176.5	0.17	10	3.67	2	0.17	10.00	3.67	2017	6.5
286	286	20176.5	0.17	10.17	3.84	2	0.17	10.17	3.84	2017	6.5
287	287	20176.5	0.17	10.5	4.17	2	0.17	10.50	4.17	2017	6.5
288	288	20176.5	1	6.5	1	3	1.00	6.50	1.00	2017	6.5
289	289	20176.5	1	7.33	1.83	3	1.00	7.33	1.83	2017	6.5
290	290	20176.5	1	7.5	2	3	1.00	7.50	2.00	2017	6.5
291	291	20176.5	1	8.5	3	3	1.00	8.50	3.00	2017	6.5
292	292	20176.5	1	9.17	3.67	3	1.00	9.17	3.67	2017	6.5
293	293	20176.5	1	9.34	3.84	3	1.00	9.34	3.84	2017	6.5
294	294	20176.5	1	9.67	4.17	3	1.00	9.67	4.17	2017	6.5
295	295	20176.5	1.83	6.5	1.83	4	1.83	6.50	1.83	2017	6.5
296	296	20176.5	1.83	6.67	2	4	1.83	6.67	2.00	2017	6.5
297	297	20176.5	1.83	7.67	3	4	1.83	7.67	3.00	2017	6.5
298	298	20176.5	1.83	8.34	3.67	4	1.83	8.34	3.67	2017	6.5
299	299	20176.5	1.83	8.51	3.84	4	1.83	8.51	3.84	2017	6.5
300	300	20176.5	1.83	8.84	4.17	4	1.83	8.84	4.17	2017	6.5
301	301	20176.5	2	6.5	2	5	2.00	6.50	2.00	2017	6.5
302	302	20176.5	2	7.5	3	5	2.00	7.50	3.00	2017	6.5
303	303	20176.5	2	8.17	3.67	5	2.00	8.17	3.67	2017	6.5
304	304	20176.5	2	8.34	3.84	5	2.00	8.34	3.84	2017	6.5
305	305	20176.5	2	8.67	4.17	5	2.00	8.67	4.17	2017	6.5
306	306	20176.5	3	6.5	3	6	3.00	6.50	3.00	2017	6.5
307	307	20176.5	3	7.17	3.67	6	3.00	7.17	3.67	2017	6.5
308	308	20176.5	3	7.34	3.84	6	3.00	7.34	3.84	2017	6.5
309	309	20176.5	3	7.67	4.17	6	3.00	7.67	4.17	2017	6.5
310	310	20176.5	3.67	6.5	3.67	7	3.67	6.50	3.67	2017	6.5
311	311	20176.5	3.67	6.67	3.84	7	3.67	6.67	3.84	2017	6.5
312	312	20176.5	3.67	7	4.17	7	3.67	7.00	4.17	2017	6.5
313	313	20176.5	3.84	6.5	3.84	8	3.84	6.50	3.84	2017	6.5
314	314	20176.5	3.84	6.83	4.17	8	3.84	6.83	4.17	2017	6.5
315	315	20176.5	4.17	6.5	4.17	9	4.17	6.50	4.17	2017	6.5
316	316	20196.5	0	6.5	0	1	0.00	6.50	0.00	2019	6.5
317	317	20196.5	0	6.67	0.17	1	0.00	6.67	0.17	2019	6.5
318	318	20196.5	0	7.5	1	1	0.00	7.50	1.00	2019	6.5
319	319	20196.5	0	8.33	1.83	1	0.00	8.33	1.83	2019	6.5
320	320	20196.5	0	8.5	2	1	0.00	8.50	2.00	2019	6.5
321	321	20196.5	0	9.5	3	1	0.00	9.50	3.00	2019	6.5
322	322	20196.5	0	10.17	3.67	1	0.00	10.17	3.67	2019	6.5
323	323	20196.5	0	10.34	3.84	1	0.00	10.34	3.84	2019	6.5
324	324	20196.5	0	10.67	4.17	1	0.00	10.67	4.17	2019	6.5
325	325	20196.5	0.17	6.5	0.17	2	0.17	6.50	0.17	2019	6.5
326	326	20196.5	0.17	7.33	1	2	0.17	7.33	1.00	2019	6.5
327	327	20196.5	0.17	8.16	1.83	2	0.17	8.16	1.83	2019	6.5
328	328	20196.5	0.17	8.33	2	2	0.17	8.33	2.00	2019	6.5
329	329	20196.5	0.17	9.33	3	2	0.17	9.33	3.00	2019	6.5
330	330	20196.5	0.17	10	3.67	2	0.17	10.00	3.67	2019	6.5
331	331	20196.5	0.17	10.17	3.84	2	0.17	10.17	3.84	2019	6.5
332	332	20196.5	0.17	10.5	4.17	2	0.17	10.50	4.17	2019	6.5
333	333	20196.5	1	6.5	1	3	1.00	6.50	1.00	2019	6.5
334	334	20196.5	1	7.33	1.83	3	1.00	7.33	1.83	2019	6.5
335	335	20196.5	1	7.5	2	3	1.00	7.50	2.00	2019	6.5
336	336	20196.5	1	8.5	3	3	1.00	8.50	3.00	2019	6.5
337	337	20196.5	1	9.17	3.67	3	1.00	9.17	3.67	2019	6.5
338	338	20196.5	1	9.34	3.84	3	1.00	9.34	3.84	2019	6.5
339	339	20196.5	1	9.67	4.17	3	1.00	9.67	4.17	2019	6.5
340	340	20196.5	1.83	6.5	1.83	4	1.83	6.50	1.83	2019	6.5
341	341	20196.5	1.83	6.67	2	4	1.83	6.67	2.00	2019	6.5
342	342	20196.5	1.83	7.67	3	4	1.83	7.67	3.00	2019	6.5
343	343	20196.5	1.83	8.34	3.67	4	1.83	8.34	3.67	2019	6.5
344	344	20196.5	1.83	8.51	3.84	4	1.83	8.51	3.84	2019	6.5
345	345	20196.5	1.83	8.84	4.17	4	1.83	8.84	4.17	2019	6.5
346	346	20196.5	2	6.5	2	5	2.00	6.50	2.00	2019	6.5
347	347	20196.5	2	7.5	3	5	2.00	7.50	3.00	2019	6.5
348	348	20196.5	2	8.17	3.67	5	2.00	8.17	3.67	2019	6.5
349	349	20196.5	2	8.34	3.84	5	2.00	8.34	3.84	2019	6.5
350	350	20196.5	2	8.67	4.17	5	2.00	8.67	4.17	2019	6.5
351	351	20196.5	3	6.5	3	6	3.00	6.50	3.00	2019	6.5
352	352	20196.5	3	7.17	3.67	6	3.00	7.17	3.67	2019	6.5
353	353	20196.5	3	7.34	3.84	6	3.00	7.34	3.84	2019	6.5
354	354	20196.5	3	7.67	4.17	6	3.00	7.67	4.17	2019	6.5
355	355	20196.5	3.67	6.5	3.67	7	3.67	6.50	3.67	2019	6.5
356	356	20196.5	3.67	6.67	3.84	7	3.67	6.67	3.84	2019	6.5
357	357	20196.5	3.67	7	4.17	7	3.67	7.00	4.17	2019	6.5
358	358	20196.5	3.84	6.5	3.84	8	3.84	6.50	3.84	2019	6.5
359	359	20196.5	3.84	6.83	4.17	8	3.84	6.83	4.17	2019	6.5
360	360	20196.5	4.17	6.5	4.17	9	4.17	6.50	4.17	2019	6.5
361	361	20157.5	0	7.5	0	1	0.00	7.50	0.00	2015	7.5
362	362	20157.5	0	7.67	0.17	1	0.00	7.67	0.17	2015	7.5
363	363	20157.5	0	8.5	1	1	0.00	8.50	1.00	2015	7.5
364	364	20157.5	0	9.33	1.83	1	0.00	9.33	1.83	2015	7.5
365	365	20157.5	0	9.5	2	1	0.00	9.50	2.00	2015	7.5
366	366	20157.5	0	10.5	3	1	0.00	10.50	3.00	2015	7.5
367	367	20157.5	0	11.17	3.67	1	0.00	11.17	3.67	2015	7.5
368	368	20157.5	0	11.34	3.84	1	0.00	11.34	3.84	2015	7.5
369	369	20157.5	0	11.67	4.17	1	0.00	11.67	4.17	2015	7.5
370	370	20157.5	0.17	7.5	0.17	2	0.17	7.50	0.17	2015	7.5
371	371	20157.5	0.17	8.33	1	2	0.17	8.33	1.00	2015	7.5
372	372	20157.5	0.17	9.16	1.83	2	0.17	9.16	1.83	2015	7.5
373	373	20157.5	0.17	9.33	2	2	0.17	9.33	2.00	2015	7.5
374	374	20157.5	0.17	10.33	3	2	0.17	10.33	3.00	2015	7.5
375	375	20157.5	0.17	11	3.67	2	0.17	11.00	3.67	2015	7.5
376	376	20157.5	0.17	11.17	3.84	2	0.17	11.17	3.84	2015	7.5
377	377	20157.5	0.17	11.5	4.17	2	0.17	11.50	4.17	2015	7.5
378	378	20157.5	1	7.5	1	3	1.00	7.50	1.00	2015	7.5
379	379	20157.5	1	8.33	1.83	3	1.00	8.33	1.83	2015	7.5
380	380	20157.5	1	8.5	2	3	1.00	8.50	2.00	2015	7.5
381	381	20157.5	1	9.5	3	3	1.00	9.50	3.00	2015	7.5
382	382	20157.5	1	10.17	3.67	3	1.00	10.17	3.67	2015	7.5
383	383	20157.5	1	10.34	3.84	3	1.00	10.34	3.84	2015	7.5
384	384	20157.5	1	10.67	4.17	3	1.00	10.67	4.17	2015	7.5
385	385	20157.5	1.83	7.5	1.83	4	1.83	7.50	1.83	2015	7.5
386	386	20157.5	1.83	7.67	2	4	1.83	7.67	2.00	2015	7.5
387	387	20157.5	1.83	8.67	3	4	1.83	8.67	3.00	2015	7.5
388	388	20157.5	1.83	9.34	3.67	4	1.83	9.34	3.67	2015	7.5
389	389	20157.5	1.83	9.51	3.84	4	1.83	9.51	3.84	2015	7.5
390	390	20157.5	1.83	9.84	4.17	4	1.83	9.84	4.17	2015	7.5
391	391	20157.5	2	7.5	2	5	2.00	7.50	2.00	2015	7.5
392	392	20157.5	2	8.5	3	5	2.00	8.50	3.00	2015	7.5
393	393	20157.5	2	9.17	3.67	5	2.00	9.17	3.67	2015	7.5
394	394	20157.5	2	9.34	3.84	5	2.00	9.34	3.84	2015	7.5
395	395	20157.5	2	9.67	4.17	5	2.00	9.67	4.17	2015	7.5
396	396	20157.5	3	7.5	3	6	3.00	7.50	3.00	2015	7.5
397	397	20157.5	3	8.17	3.67	6	3.00	8.17	3.67	2015	7.5
398	398	20157.5	3	8.34	3.84	6	3.00	8.34	3.84	2015	7.5
399	399	20157.5	3	8.67	4.17	6	3.00	8.67	4.17	2015	7.5
400	400	20157.5	3.67	7.5	3.67	7	3.67	7.50	3.67	2015	7.5
401	401	20157.5	3.67	7.67	3.84	7	3.67	7.67	3.84	2015	7.5
402	402	20157.5	3.67	8	4.17	7	3.67	8.00	4.17	2015	7.5
403	403	20157.5	3.84	7.5	3.84	8	3.84	7.50	3.84	2015	7.5
404	404	20157.5	3.84	7.83	4.17	8	3.84	7.83	4.17	2015	7.5
405	405	20157.5	4.17	7.5	4.17	9	4.17	7.50	4.17	2015	7.5
406	406	20177.5	0	7.5	0	1	0.00	7.50	0.00	2017	7.5
407	407	20177.5	0	7.67	0.17	1	0.00	7.67	0.17	2017	7.5
408	408	20177.5	0	8.5	1	1	0.00	8.50	1.00	2017	7.5
409	409	20177.5	0	9.33	1.83	1	0.00	9.33	1.83	2017	7.5
410	410	20177.5	0	9.5	2	1	0.00	9.50	2.00	2017	7.5
411	411	20177.5	0	10.5	3	1	0.00	10.50	3.00	2017	7.5
412	412	20177.5	0	11.17	3.67	1	0.00	11.17	3.67	2017	7.5
413	413	20177.5	0	11.34	3.84	1	0.00	11.34	3.84	2017	7.5
414	414	20177.5	0	11.67	4.17	1	0.00	11.67	4.17	2017	7.5
415	415	20177.5	0.17	7.5	0.17	2	0.17	7.50	0.17	2017	7.5
416	416	20177.5	0.17	8.33	1	2	0.17	8.33	1.00	2017	7.5
417	417	20177.5	0.17	9.16	1.83	2	0.17	9.16	1.83	2017	7.5
418	418	20177.5	0.17	9.33	2	2	0.17	9.33	2.00	2017	7.5
419	419	20177.5	0.17	10.33	3	2	0.17	10.33	3.00	2017	7.5
420	420	20177.5	0.17	11	3.67	2	0.17	11.00	3.67	2017	7.5
421	421	20177.5	0.17	11.17	3.84	2	0.17	11.17	3.84	2017	7.5
422	422	20177.5	0.17	11.5	4.17	2	0.17	11.50	4.17	2017	7.5
423	423	20177.5	1	7.5	1	3	1.00	7.50	1.00	2017	7.5
424	424	20177.5	1	8.33	1.83	3	1.00	8.33	1.83	2017	7.5
425	425	20177.5	1	8.5	2	3	1.00	8.50	2.00	2017	7.5
426	426	20177.5	1	9.5	3	3	1.00	9.50	3.00	2017	7.5
427	427	20177.5	1	10.17	3.67	3	1.00	10.17	3.67	2017	7.5
428	428	20177.5	1	10.34	3.84	3	1.00	10.34	3.84	2017	7.5
429	429	20177.5	1	10.67	4.17	3	1.00	10.67	4.17	2017	7.5
430	430	20177.5	1.83	7.5	1.83	4	1.83	7.50	1.83	2017	7.5
431	431	20177.5	1.83	7.67	2	4	1.83	7.67	2.00	2017	7.5
432	432	20177.5	1.83	8.67	3	4	1.83	8.67	3.00	2017	7.5
433	433	20177.5	1.83	9.34	3.67	4	1.83	9.34	3.67	2017	7.5
434	434	20177.5	1.83	9.51	3.84	4	1.83	9.51	3.84	2017	7.5
435	435	20177.5	1.83	9.84	4.17	4	1.83	9.84	4.17	2017	7.5
436	436	20177.5	2	7.5	2	5	2.00	7.50	2.00	2017	7.5
437	437	20177.5	2	8.5	3	5	2.00	8.50	3.00	2017	7.5
438	438	20177.5	2	9.17	3.67	5	2.00	9.17	3.67	2017	7.5
439	439	20177.5	2	9.34	3.84	5	2.00	9.34	3.84	2017	7.5
440	440	20177.5	2	9.67	4.17	5	2.00	9.67	4.17	2017	7.5
441	441	20177.5	3	7.5	3	6	3.00	7.50	3.00	2017	7.5
442	442	20177.5	3	8.17	3.67	6	3.00	8.17	3.67	2017	7.5
443	443	20177.5	3	8.34	3.84	6	3.00	8.34	3.84	2017	7.5
444	444	20177.5	3	8.67	4.17	6	3.00	8.67	4.17	2017	7.5
445	445	20177.5	3.67	7.5	3.67	7	3.67	7.50	3.67	2017	7.5
446	446	20177.5	3.67	7.67	3.84	7	3.67	7.67	3.84	2017	7.5
447	447	20177.5	3.67	8	4.17	7	3.67	8.00	4.17	2017	7.5
448	448	20177.5	3.84	7.5	3.84	8	3.84	7.50	3.84	2017	7.5
449	449	20177.5	3.84	7.83	4.17	8	3.84	7.83	4.17	2017	7.5
450	450	20177.5	4.17	7.5	4.17	9	4.17	7.50	4.17	2017	7.5
451	451	20197.5	0	7.5	0	1	0.00	7.50	0.00	2019	7.5
452	452	20197.5	0	7.67	0.17	1	0.00	7.67	0.17	2019	7.5
453	453	20197.5	0	8.5	1	1	0.00	8.50	1.00	2019	7.5
454	454	20197.5	0	9.33	1.83	1	0.00	9.33	1.83	2019	7.5
455	455	20197.5	0	9.5	2	1	0.00	9.50	2.00	2019	7.5
456	456	20197.5	0	10.5	3	1	0.00	10.50	3.00	2019	7.5
457	457	20197.5	0	11.17	3.67	1	0.00	11.17	3.67	2019	7.5
458	458	20197.5	0	11.34	3.84	1	0.00	11.34	3.84	2019	7.5
459	459	20197.5	0	11.67	4.17	1	0.00	11.67	4.17	2019	7.5
460	460	20197.5	0.17	7.5	0.17	2	0.17	7.50	0.17	2019	7.5
461	461	20197.5	0.17	8.33	1	2	0.17	8.33	1.00	2019	7.5
462	462	20197.5	0.17	9.16	1.83	2	0.17	9.16	1.83	2019	7.5
463	463	20197.5	0.17	9.33	2	2	0.17	9.33	2.00	2019	7.5
464	464	20197.5	0.17	10.33	3	2	0.17	10.33	3.00	2019	7.5
465	465	20197.5	0.17	11	3.67	2	0.17	11.00	3.67	2019	7.5
466	466	20197.5	0.17	11.17	3.84	2	0.17	11.17	3.84	2019	7.5
467	467	20197.5	0.17	11.5	4.17	2	0.17	11.50	4.17	2019	7.5
468	468	20197.5	1	7.5	1	3	1.00	7.50	1.00	2019	7.5
469	469	20197.5	1	8.33	1.83	3	1.00	8.33	1.83	2019	7.5
470	470	20197.5	1	8.5	2	3	1.00	8.50	2.00	2019	7.5
471	471	20197.5	1	9.5	3	3	1.00	9.50	3.00	2019	7.5
472	472	20197.5	1	10.17	3.67	3	1.00	10.17	3.67	2019	7.5
473	473	20197.5	1	10.34	3.84	3	1.00	10.34	3.84	2019	7.5
474	474	20197.5	1	10.67	4.17	3	1.00	10.67	4.17	2019	7.5
475	475	20197.5	1.83	7.5	1.83	4	1.83	7.50	1.83	2019	7.5
476	476	20197.5	1.83	7.67	2	4	1.83	7.67	2.00	2019	7.5
477	477	20197.5	1.83	8.67	3	4	1.83	8.67	3.00	2019	7.5
478	478	20197.5	1.83	9.34	3.67	4	1.83	9.34	3.67	2019	7.5
479	479	20197.5	1.83	9.51	3.84	4	1.83	9.51	3.84	2019	7.5
480	480	20197.5	1.83	9.84	4.17	4	1.83	9.84	4.17	2019	7.5
481	481	20197.5	2	7.5	2	5	2.00	7.50	2.00	2019	7.5
482	482	20197.5	2	8.5	3	5	2.00	8.50	3.00	2019	7.5
483	483	20197.5	2	9.17	3.67	5	2.00	9.17	3.67	2019	7.5
484	484	20197.5	2	9.34	3.84	5	2.00	9.34	3.84	2019	7.5
485	485	20197.5	2	9.67	4.17	5	2.00	9.67	4.17	2019	7.5
486	486	20197.5	3	7.5	3	6	3.00	7.50	3.00	2019	7.5
487	487	20197.5	3	8.17	3.67	6	3.00	8.17	3.67	2019	7.5
488	488	20197.5	3	8.34	3.84	6	3.00	8.34	3.84	2019	7.5
489	489	20197.5	3	8.67	4.17	6	3.00	8.67	4.17	2019	7.5
490	490	20197.5	3.67	7.5	3.67	7	3.67	7.50	3.67	2019	7.5
491	491	20197.5	3.67	7.67	3.84	7	3.67	7.67	3.84	2019	7.5
492	492	20197.5	3.67	8	4.17	7	3.67	8.00	4.17	2019	7.5
493	493	20197.5	3.84	7.5	3.84	8	3.84	7.50	3.84	2019	7.5
494	494	20197.5	3.84	7.83	4.17	8	3.84	7.83	4.17	2019	7.5
495	495	20197.5	4.17	7.5	4.17	9	4.17	7.50	4.17	2019	7.5
496	496	20158.5	0	8.5	0	1	0.00	8.50	0.00	2015	8.5
497	497	20158.5	0	8.67	0.17	1	0.00	8.67	0.17	2015	8.5
498	498	20158.5	0	9.5	1	1	0.00	9.50	1.00	2015	8.5
499	499	20158.5	0	10.33	1.83	1	0.00	10.33	1.83	2015	8.5
500	500	20158.5	0	10.5	2	1	0.00	10.50	2.00	2015	8.5
501	501	20158.5	0	11.5	3	1	0.00	11.50	3.00	2015	8.5
502	502	20158.5	0	12.17	3.67	1	0.00	12.17	3.67	2015	8.5
503	503	20158.5	0	12.34	3.84	1	0.00	12.34	3.84	2015	8.5
504	504	20158.5	0	12.67	4.17	1	0.00	12.67	4.17	2015	8.5
505	505	20158.5	0.17	8.5	0.17	2	0.17	8.50	0.17	2015	8.5
506	506	20158.5	0.17	9.33	1	2	0.17	9.33	1.00	2015	8.5
507	507	20158.5	0.17	10.16	1.83	2	0.17	10.16	1.83	2015	8.5
508	508	20158.5	0.17	10.33	2	2	0.17	10.33	2.00	2015	8.5
509	509	20158.5	0.17	11.33	3	2	0.17	11.33	3.00	2015	8.5
510	510	20158.5	0.17	12	3.67	2	0.17	12.00	3.67	2015	8.5
511	511	20158.5	0.17	12.17	3.84	2	0.17	12.17	3.84	2015	8.5
512	512	20158.5	0.17	12.5	4.17	2	0.17	12.50	4.17	2015	8.5
513	513	20158.5	1	8.5	1	3	1.00	8.50	1.00	2015	8.5
514	514	20158.5	1	9.33	1.83	3	1.00	9.33	1.83	2015	8.5
515	515	20158.5	1	9.5	2	3	1.00	9.50	2.00	2015	8.5
516	516	20158.5	1	10.5	3	3	1.00	10.50	3.00	2015	8.5
517	517	20158.5	1	11.17	3.67	3	1.00	11.17	3.67	2015	8.5
518	518	20158.5	1	11.34	3.84	3	1.00	11.34	3.84	2015	8.5
519	519	20158.5	1	11.67	4.17	3	1.00	11.67	4.17	2015	8.5
520	520	20158.5	1.83	8.5	1.83	4	1.83	8.50	1.83	2015	8.5
521	521	20158.5	1.83	8.67	2	4	1.83	8.67	2.00	2015	8.5
522	522	20158.5	1.83	9.67	3	4	1.83	9.67	3.00	2015	8.5
523	523	20158.5	1.83	10.34	3.67	4	1.83	10.34	3.67	2015	8.5
524	524	20158.5	1.83	10.51	3.84	4	1.83	10.51	3.84	2015	8.5
525	525	20158.5	1.83	10.84	4.17	4	1.83	10.84	4.17	2015	8.5
526	526	20158.5	2	8.5	2	5	2.00	8.50	2.00	2015	8.5
527	527	20158.5	2	9.5	3	5	2.00	9.50	3.00	2015	8.5
528	528	20158.5	2	10.17	3.67	5	2.00	10.17	3.67	2015	8.5
529	529	20158.5	2	10.34	3.84	5	2.00	10.34	3.84	2015	8.5
530	530	20158.5	2	10.67	4.17	5	2.00	10.67	4.17	2015	8.5
531	531	20158.5	3	8.5	3	6	3.00	8.50	3.00	2015	8.5
532	532	20158.5	3	9.17	3.67	6	3.00	9.17	3.67	2015	8.5
533	533	20158.5	3	9.34	3.84	6	3.00	9.34	3.84	2015	8.5
534	534	20158.5	3	9.67	4.17	6	3.00	9.67	4.17	2015	8.5
535	535	20158.5	3.67	8.5	3.67	7	3.67	8.50	3.67	2015	8.5
536	536	20158.5	3.67	8.67	3.84	7	3.67	8.67	3.84	2015	8.5
537	537	20158.5	3.67	9	4.17	7	3.67	9.00	4.17	2015	8.5
538	538	20158.5	3.84	8.5	3.84	8	3.84	8.50	3.84	2015	8.5
539	539	20158.5	3.84	8.83	4.17	8	3.84	8.83	4.17	2015	8.5
540	540	20158.5	4.17	8.5	4.17	9	4.17	8.50	4.17	2015	8.5
541	541	20198.5	0	8.5	0	1	0.00	8.50	0.00	2019	8.5
542	542	20198.5	0	8.67	0.17	1	0.00	8.67	0.17	2019	8.5
543	543	20198.5	0	9.5	1	1	0.00	9.50	1.00	2019	8.5
544	544	20198.5	0	10.33	1.83	1	0.00	10.33	1.83	2019	8.5
545	545	20198.5	0	10.5	2	1	0.00	10.50	2.00	2019	8.5
546	546	20198.5	0	11.5	3	1	0.00	11.50	3.00	2019	8.5
547	547	20198.5	0	12.17	3.67	1	0.00	12.17	3.67	2019	8.5
548	548	20198.5	0	12.34	3.84	1	0.00	12.34	3.84	2019	8.5
549	549	20198.5	0	12.67	4.17	1	0.00	12.67	4.17	2019	8.5
550	550	20198.5	0.17	8.5	0.17	2	0.17	8.50	0.17	2019	8.5
551	551	20198.5	0.17	9.33	1	2	0.17	9.33	1.00	2019	8.5
552	552	20198.5	0.17	10.16	1.83	2	0.17	10.16	1.83	2019	8.5
553	553	20198.5	0.17	10.33	2	2	0.17	10.33	2.00	2019	8.5
554	554	20198.5	0.17	11.33	3	2	0.17	11.33	3.00	2019	8.5
555	555	20198.5	0.17	12	3.67	2	0.17	12.00	3.67	2019	8.5
556	556	20198.5	0.17	12.17	3.84	2	0.17	12.17	3.84	2019	8.5
557	557	20198.5	0.17	12.5	4.17	2	0.17	12.50	4.17	2019	8.5
558	558	20198.5	1	8.5	1	3	1.00	8.50	1.00	2019	8.5
559	559	20198.5	1	9.33	1.83	3	1.00	9.33	1.83	2019	8.5
560	560	20198.5	1	9.5	2	3	1.00	9.50	2.00	2019	8.5
561	561	20198.5	1	10.5	3	3	1.00	10.50	3.00	2019	8.5
562	562	20198.5	1	11.17	3.67	3	1.00	11.17	3.67	2019	8.5
563	563	20198.5	1	11.34	3.84	3	1.00	11.34	3.84	2019	8.5
564	564	20198.5	1	11.67	4.17	3	1.00	11.67	4.17	2019	8.5
565	565	20198.5	1.83	8.5	1.83	4	1.83	8.50	1.83	2019	8.5
566	566	20198.5	1.83	8.67	2	4	1.83	8.67	2.00	2019	8.5
567	567	20198.5	1.83	9.67	3	4	1.83	9.67	3.00	2019	8.5
568	568	20198.5	1.83	10.34	3.67	4	1.83	10.34	3.67	2019	8.5
569	569	20198.5	1.83	10.51	3.84	4	1.83	10.51	3.84	2019	8.5
570	570	20198.5	1.83	10.84	4.17	4	1.83	10.84	4.17	2019	8.5
571	571	20198.5	2	8.5	2	5	2.00	8.50	2.00	2019	8.5
572	572	20198.5	2	9.5	3	5	2.00	9.50	3.00	2019	8.5
573	573	20198.5	2	10.17	3.67	5	2.00	10.17	3.67	2019	8.5
574	574	20198.5	2	10.34	3.84	5	2.00	10.34	3.84	2019	8.5
575	575	20198.5	2	10.67	4.17	5	2.00	10.67	4.17	2019	8.5
576	576	20198.5	3	8.5	3	6	3.00	8.50	3.00	2019	8.5
577	577	20198.5	3	9.17	3.67	6	3.00	9.17	3.67	2019	8.5
578	578	20198.5	3	9.34	3.84	6	3.00	9.34	3.84	2019	8.5
579	579	20198.5	3	9.67	4.17	6	3.00	9.67	4.17	2019	8.5
580	580	20198.5	3.67	8.5	3.67	7	3.67	8.50	3.67	2019	8.5
581	581	20198.5	3.67	8.67	3.84	7	3.67	8.67	3.84	2019	8.5
582	582	20198.5	3.67	9	4.17	7	3.67	9.00	4.17	2019	8.5
583	583	20198.5	3.84	8.5	3.84	8	3.84	8.50	3.84	2019	8.5
584	584	20198.5	3.84	8.83	4.17	8	3.84	8.83	4.17	2019	8.5
585	585	20198.5	4.17	8.5	4.17	9	4.17	8.50	4.17	2019	8.5
586	586	20159.5	0	9.5	0	1	0.00	9.50	0.00	2015	9.5
587	587	20159.5	0	9.67	0.17	1	0.00	9.67	0.17	2015	9.5
588	588	20159.5	0	10.5	1	1	0.00	10.50	1.00	2015	9.5
589	589	20159.5	0	11.33	1.83	1	0.00	11.33	1.83	2015	9.5
590	590	20159.5	0	11.5	2	1	0.00	11.50	2.00	2015	9.5
591	591	20159.5	0	12.5	3	1	0.00	12.50	3.00	2015	9.5
592	592	20159.5	0	13.17	3.67	1	0.00	13.17	3.67	2015	9.5
593	593	20159.5	0	13.34	3.84	1	0.00	13.34	3.84	2015	9.5
594	594	20159.5	0	13.67	4.17	1	0.00	13.67	4.17	2015	9.5
595	595	20159.5	0.17	9.5	0.17	2	0.17	9.50	0.17	2015	9.5
596	596	20159.5	0.17	10.33	1	2	0.17	10.33	1.00	2015	9.5
597	597	20159.5	0.17	11.16	1.83	2	0.17	11.16	1.83	2015	9.5
598	598	20159.5	0.17	11.33	2	2	0.17	11.33	2.00	2015	9.5
599	599	20159.5	0.17	12.33	3	2	0.17	12.33	3.00	2015	9.5
600	600	20159.5	0.17	13	3.67	2	0.17	13.00	3.67	2015	9.5
601	601	20159.5	0.17	13.17	3.84	2	0.17	13.17	3.84	2015	9.5
602	602	20159.5	0.17	13.5	4.17	2	0.17	13.50	4.17	2015	9.5
603	603	20159.5	1	9.5	1	3	1.00	9.50	1.00	2015	9.5
604	604	20159.5	1	10.33	1.83	3	1.00	10.33	1.83	2015	9.5
605	605	20159.5	1	10.5	2	3	1.00	10.50	2.00	2015	9.5
606	606	20159.5	1	11.5	3	3	1.00	11.50	3.00	2015	9.5
607	607	20159.5	1	12.17	3.67	3	1.00	12.17	3.67	2015	9.5
608	608	20159.5	1	12.34	3.84	3	1.00	12.34	3.84	2015	9.5
609	609	20159.5	1	12.67	4.17	3	1.00	12.67	4.17	2015	9.5
610	610	20159.5	1.83	9.5	1.83	4	1.83	9.50	1.83	2015	9.5
611	611	20159.5	1.83	9.67	2	4	1.83	9.67	2.00	2015	9.5
612	612	20159.5	1.83	10.67	3	4	1.83	10.67	3.00	2015	9.5
613	613	20159.5	1.83	11.34	3.67	4	1.83	11.34	3.67	2015	9.5
614	614	20159.5	1.83	11.51	3.84	4	1.83	11.51	3.84	2015	9.5
615	615	20159.5	1.83	11.84	4.17	4	1.83	11.84	4.17	2015	9.5
616	616	20159.5	2	9.5	2	5	2.00	9.50	2.00	2015	9.5
617	617	20159.5	2	10.5	3	5	2.00	10.50	3.00	2015	9.5
618	618	20159.5	2	11.17	3.67	5	2.00	11.17	3.67	2015	9.5
619	619	20159.5	2	11.34	3.84	5	2.00	11.34	3.84	2015	9.5
620	620	20159.5	2	11.67	4.17	5	2.00	11.67	4.17	2015	9.5
621	621	20159.5	3	9.5	3	6	3.00	9.50	3.00	2015	9.5
622	622	20159.5	3	10.17	3.67	6	3.00	10.17	3.67	2015	9.5
623	623	20159.5	3	10.34	3.84	6	3.00	10.34	3.84	2015	9.5
624	624	20159.5	3	10.67	4.17	6	3.00	10.67	4.17	2015	9.5
625	625	20159.5	3.67	9.5	3.67	7	3.67	9.50	3.67	2015	9.5
626	626	20159.5	3.67	9.67	3.84	7	3.67	9.67	3.84	2015	9.5
627	627	20159.5	3.67	10	4.17	7	3.67	10.00	4.17	2015	9.5
628	628	20159.5	3.84	9.5	3.84	8	3.84	9.50	3.84	2015	9.5
629	629	20159.5	3.84	9.83	4.17	8	3.84	9.83	4.17	2015	9.5
630	630	20159.5	4.17	9.5	4.17	9	4.17	9.50	4.17	2015	9.5
631	631	201510.5	0	10.5	0	1	0.00	10.50	0.00	2015	10.5
632	632	201510.5	0	10.67	0.17	1	0.00	10.67	0.17	2015	10.5
633	633	201510.5	0	11.5	1	1	0.00	11.50	1.00	2015	10.5
634	634	201510.5	0	12.33	1.83	1	0.00	12.33	1.83	2015	10.5
635	635	201510.5	0	12.5	2	1	0.00	12.50	2.00	2015	10.5
636	636	201510.5	0	13.5	3	1	0.00	13.50	3.00	2015	10.5
637	637	201510.5	0	14.17	3.67	1	0.00	14.17	3.67	2015	10.5
638	638	201510.5	0	14.34	3.84	1	0.00	14.34	3.84	2015	10.5
639	639	201510.5	0	14.67	4.17	1	0.00	14.67	4.17	2015	10.5
640	640	201510.5	0.17	10.5	0.17	2	0.17	10.50	0.17	2015	10.5
641	641	201510.5	0.17	11.33	1	2	0.17	11.33	1.00	2015	10.5
642	642	201510.5	0.17	12.16	1.83	2	0.17	12.16	1.83	2015	10.5
643	643	201510.5	0.17	12.33	2	2	0.17	12.33	2.00	2015	10.5
644	644	201510.5	0.17	13.33	3	2	0.17	13.33	3.00	2015	10.5
645	645	201510.5	0.17	14	3.67	2	0.17	14.00	3.67	2015	10.5
646	646	201510.5	0.17	14.17	3.84	2	0.17	14.17	3.84	2015	10.5
647	647	201510.5	0.17	14.5	4.17	2	0.17	14.50	4.17	2015	10.5
648	648	201510.5	1	10.5	1	3	1.00	10.50	1.00	2015	10.5
649	649	201510.5	1	11.33	1.83	3	1.00	11.33	1.83	2015	10.5
650	650	201510.5	1	11.5	2	3	1.00	11.50	2.00	2015	10.5
651	651	201510.5	1	12.5	3	3	1.00	12.50	3.00	2015	10.5
652	652	201510.5	1	13.17	3.67	3	1.00	13.17	3.67	2015	10.5
653	653	201510.5	1	13.34	3.84	3	1.00	13.34	3.84	2015	10.5
654	654	201510.5	1	13.67	4.17	3	1.00	13.67	4.17	2015	10.5
655	655	201510.5	1.83	10.5	1.83	4	1.83	10.50	1.83	2015	10.5
656	656	201510.5	1.83	10.67	2	4	1.83	10.67	2.00	2015	10.5
657	657	201510.5	1.83	11.67	3	4	1.83	11.67	3.00	2015	10.5
658	658	201510.5	1.83	12.34	3.67	4	1.83	12.34	3.67	2015	10.5
659	659	201510.5	1.83	12.51	3.84	4	1.83	12.51	3.84	2015	10.5
660	660	201510.5	1.83	12.84	4.17	4	1.83	12.84	4.17	2015	10.5
661	661	201510.5	2	10.5	2	5	2.00	10.50	2.00	2015	10.5
662	662	201510.5	2	11.5	3	5	2.00	11.50	3.00	2015	10.5
663	663	201510.5	2	12.17	3.67	5	2.00	12.17	3.67	2015	10.5
664	664	201510.5	2	12.34	3.84	5	2.00	12.34	3.84	2015	10.5
665	665	201510.5	2	12.67	4.17	5	2.00	12.67	4.17	2015	10.5
666	666	201510.5	3	10.5	3	6	3.00	10.50	3.00	2015	10.5
667	667	201510.5	3	11.17	3.67	6	3.00	11.17	3.67	2015	10.5
668	668	201510.5	3	11.34	3.84	6	3.00	11.34	3.84	2015	10.5
669	669	201510.5	3	11.67	4.17	6	3.00	11.67	4.17	2015	10.5
670	670	201510.5	3.67	10.5	3.67	7	3.67	10.50	3.67	2015	10.5
671	671	201510.5	3.67	10.67	3.84	7	3.67	10.67	3.84	2015	10.5
672	672	201510.5	3.67	11	4.17	7	3.67	11.00	4.17	2015	10.5
673	673	201510.5	3.84	10.5	3.84	8	3.84	10.50	3.84	2015	10.5
674	674	201510.5	3.84	10.83	4.17	8	3.84	10.83	4.17	2015	10.5
675	675	201510.5	4.17	10.5	4.17	9	4.17	10.50	4.17	2015	10.5

kable(tortoises.ddl[[2]][], "html", 
      caption = "PIMS for p (detection) parameter") %>% 
  kable_styling(bootstrap_options = c("striped", "condensed")) %>%
  scroll_box(height = "300px")

PIMS for p (detection) parameter

time	par.index	model.index	group	cohort	age	occ.cohort	Cohort	Age	Time	release_cohort	age_release	effort	fix
0.17	1	676	20154.5	0	4.67	1	0.00	4.67	0.00	2015	4.5	24	NA
1	2	677	20154.5	0	5.5	1	0.00	5.50	0.83	2015	4.5	36	NA
1.83	3	678	20154.5	0	6.33	1	0.00	6.33	1.66	2015	4.5	0	0
2	4	679	20154.5	0	6.5	1	0.00	6.50	1.83	2015	4.5	20	NA
3	5	680	20154.5	0	7.5	1	0.00	7.50	2.83	2015	4.5	24	NA
3.67	6	681	20154.5	0	8.17	1	0.00	8.17	3.50	2015	4.5	0	0
3.84	7	682	20154.5	0	8.34	1	0.00	8.34	3.67	2015	4.5	74	NA
4.17	8	683	20154.5	0	8.67	1	0.00	8.67	4.00	2015	4.5	24	NA
4.75	9	684	20154.5	0	9.25	1	0.00	9.25	4.58	2015	4.5	16	NA
1	10	685	20154.5	0.17	5.33	2	0.17	5.33	0.83	2015	4.5	36	NA
1.83	11	686	20154.5	0.17	6.16	2	0.17	6.16	1.66	2015	4.5	0	0
2	12	687	20154.5	0.17	6.33	2	0.17	6.33	1.83	2015	4.5	20	NA
3	13	688	20154.5	0.17	7.33	2	0.17	7.33	2.83	2015	4.5	24	NA
3.67	14	689	20154.5	0.17	8	2	0.17	8.00	3.50	2015	4.5	0	0
3.84	15	690	20154.5	0.17	8.17	2	0.17	8.17	3.67	2015	4.5	74	NA
4.17	16	691	20154.5	0.17	8.5	2	0.17	8.50	4.00	2015	4.5	24	NA
4.75	17	692	20154.5	0.17	9.08	2	0.17	9.08	4.58	2015	4.5	16	NA
1.83	18	693	20154.5	1	5.33	3	1.00	5.33	1.66	2015	4.5	0	0
2	19	694	20154.5	1	5.5	3	1.00	5.50	1.83	2015	4.5	20	NA
3	20	695	20154.5	1	6.5	3	1.00	6.50	2.83	2015	4.5	24	NA
3.67	21	696	20154.5	1	7.17	3	1.00	7.17	3.50	2015	4.5	0	0
3.84	22	697	20154.5	1	7.34	3	1.00	7.34	3.67	2015	4.5	74	NA
4.17	23	698	20154.5	1	7.67	3	1.00	7.67	4.00	2015	4.5	24	NA
4.75	24	699	20154.5	1	8.25	3	1.00	8.25	4.58	2015	4.5	16	NA
2	25	700	20154.5	1.83	4.67	4	1.83	4.67	1.83	2015	4.5	20	NA
3	26	701	20154.5	1.83	5.67	4	1.83	5.67	2.83	2015	4.5	24	NA
3.67	27	702	20154.5	1.83	6.34	4	1.83	6.34	3.50	2015	4.5	0	0
3.84	28	703	20154.5	1.83	6.51	4	1.83	6.51	3.67	2015	4.5	74	NA
4.17	29	704	20154.5	1.83	6.84	4	1.83	6.84	4.00	2015	4.5	24	NA
4.75	30	705	20154.5	1.83	7.42	4	1.83	7.42	4.58	2015	4.5	16	NA
3	31	706	20154.5	2	5.5	5	2.00	5.50	2.83	2015	4.5	24	NA
3.67	32	707	20154.5	2	6.17	5	2.00	6.17	3.50	2015	4.5	0	0
3.84	33	708	20154.5	2	6.34	5	2.00	6.34	3.67	2015	4.5	74	NA
4.17	34	709	20154.5	2	6.67	5	2.00	6.67	4.00	2015	4.5	24	NA
4.75	35	710	20154.5	2	7.25	5	2.00	7.25	4.58	2015	4.5	16	NA
3.67	36	711	20154.5	3	5.17	6	3.00	5.17	3.50	2015	4.5	0	0
3.84	37	712	20154.5	3	5.34	6	3.00	5.34	3.67	2015	4.5	74	NA
4.17	38	713	20154.5	3	5.67	6	3.00	5.67	4.00	2015	4.5	24	NA
4.75	39	714	20154.5	3	6.25	6	3.00	6.25	4.58	2015	4.5	16	NA
3.84	40	715	20154.5	3.67	4.67	7	3.67	4.67	3.67	2015	4.5	74	NA
4.17	41	716	20154.5	3.67	5	7	3.67	5.00	4.00	2015	4.5	24	NA
4.75	42	717	20154.5	3.67	5.58	7	3.67	5.58	4.58	2015	4.5	16	NA
4.17	43	718	20154.5	3.84	4.83	8	3.84	4.83	4.00	2015	4.5	24	NA
4.75	44	719	20154.5	3.84	5.41	8	3.84	5.41	4.58	2015	4.5	16	NA
4.75	45	720	20154.5	4.17	5.08	9	4.17	5.08	4.58	2015	4.5	16	NA
0.17	46	721	20174.5	0	4.67	1	0.00	4.67	0.00	2017	4.5	24	NA
1	47	722	20174.5	0	5.5	1	0.00	5.50	0.83	2017	4.5	36	NA
1.83	48	723	20174.5	0	6.33	1	0.00	6.33	1.66	2017	4.5	0	NA
2	49	724	20174.5	0	6.5	1	0.00	6.50	1.83	2017	4.5	20	NA
3	50	725	20174.5	0	7.5	1	0.00	7.50	2.83	2017	4.5	24	NA
3.67	51	726	20174.5	0	8.17	1	0.00	8.17	3.50	2017	4.5	0	0
3.84	52	727	20174.5	0	8.34	1	0.00	8.34	3.67	2017	4.5	74	NA
4.17	53	728	20174.5	0	8.67	1	0.00	8.67	4.00	2017	4.5	24	NA
4.75	54	729	20174.5	0	9.25	1	0.00	9.25	4.58	2017	4.5	16	NA
1	55	730	20174.5	0.17	5.33	2	0.17	5.33	0.83	2017	4.5	36	NA
1.83	56	731	20174.5	0.17	6.16	2	0.17	6.16	1.66	2017	4.5	0	NA
2	57	732	20174.5	0.17	6.33	2	0.17	6.33	1.83	2017	4.5	20	NA
3	58	733	20174.5	0.17	7.33	2	0.17	7.33	2.83	2017	4.5	24	NA
3.67	59	734	20174.5	0.17	8	2	0.17	8.00	3.50	2017	4.5	0	0
3.84	60	735	20174.5	0.17	8.17	2	0.17	8.17	3.67	2017	4.5	74	NA
4.17	61	736	20174.5	0.17	8.5	2	0.17	8.50	4.00	2017	4.5	24	NA
4.75	62	737	20174.5	0.17	9.08	2	0.17	9.08	4.58	2017	4.5	16	NA
1.83	63	738	20174.5	1	5.33	3	1.00	5.33	1.66	2017	4.5	0	NA
2	64	739	20174.5	1	5.5	3	1.00	5.50	1.83	2017	4.5	20	NA
3	65	740	20174.5	1	6.5	3	1.00	6.50	2.83	2017	4.5	24	NA
3.67	66	741	20174.5	1	7.17	3	1.00	7.17	3.50	2017	4.5	0	0
3.84	67	742	20174.5	1	7.34	3	1.00	7.34	3.67	2017	4.5	74	NA
4.17	68	743	20174.5	1	7.67	3	1.00	7.67	4.00	2017	4.5	24	NA
4.75	69	744	20174.5	1	8.25	3	1.00	8.25	4.58	2017	4.5	16	NA
2	70	745	20174.5	1.83	4.67	4	1.83	4.67	1.83	2017	4.5	20	NA
3	71	746	20174.5	1.83	5.67	4	1.83	5.67	2.83	2017	4.5	24	NA
3.67	72	747	20174.5	1.83	6.34	4	1.83	6.34	3.50	2017	4.5	0	0
3.84	73	748	20174.5	1.83	6.51	4	1.83	6.51	3.67	2017	4.5	74	NA
4.17	74	749	20174.5	1.83	6.84	4	1.83	6.84	4.00	2017	4.5	24	NA
4.75	75	750	20174.5	1.83	7.42	4	1.83	7.42	4.58	2017	4.5	16	NA
3	76	751	20174.5	2	5.5	5	2.00	5.50	2.83	2017	4.5	24	NA
3.67	77	752	20174.5	2	6.17	5	2.00	6.17	3.50	2017	4.5	0	0
3.84	78	753	20174.5	2	6.34	5	2.00	6.34	3.67	2017	4.5	74	NA
4.17	79	754	20174.5	2	6.67	5	2.00	6.67	4.00	2017	4.5	24	NA
4.75	80	755	20174.5	2	7.25	5	2.00	7.25	4.58	2017	4.5	16	NA
3.67	81	756	20174.5	3	5.17	6	3.00	5.17	3.50	2017	4.5	0	0
3.84	82	757	20174.5	3	5.34	6	3.00	5.34	3.67	2017	4.5	74	NA
4.17	83	758	20174.5	3	5.67	6	3.00	5.67	4.00	2017	4.5	24	NA
4.75	84	759	20174.5	3	6.25	6	3.00	6.25	4.58	2017	4.5	16	NA
3.84	85	760	20174.5	3.67	4.67	7	3.67	4.67	3.67	2017	4.5	74	NA
4.17	86	761	20174.5	3.67	5	7	3.67	5.00	4.00	2017	4.5	24	NA
4.75	87	762	20174.5	3.67	5.58	7	3.67	5.58	4.58	2017	4.5	16	NA
4.17	88	763	20174.5	3.84	4.83	8	3.84	4.83	4.00	2017	4.5	24	NA
4.75	89	764	20174.5	3.84	5.41	8	3.84	5.41	4.58	2017	4.5	16	NA
4.75	90	765	20174.5	4.17	5.08	9	4.17	5.08	4.58	2017	4.5	16	NA
0.17	91	766	20155.5	0	5.67	1	0.00	5.67	0.00	2015	5.5	24	NA
1	92	767	20155.5	0	6.5	1	0.00	6.50	0.83	2015	5.5	36	NA
1.83	93	768	20155.5	0	7.33	1	0.00	7.33	1.66	2015	5.5	0	0
2	94	769	20155.5	0	7.5	1	0.00	7.50	1.83	2015	5.5	20	NA
3	95	770	20155.5	0	8.5	1	0.00	8.50	2.83	2015	5.5	24	NA
3.67	96	771	20155.5	0	9.17	1	0.00	9.17	3.50	2015	5.5	0	0
3.84	97	772	20155.5	0	9.34	1	0.00	9.34	3.67	2015	5.5	74	NA
4.17	98	773	20155.5	0	9.67	1	0.00	9.67	4.00	2015	5.5	24	NA
4.75	99	774	20155.5	0	10.25	1	0.00	10.25	4.58	2015	5.5	16	NA
1	100	775	20155.5	0.17	6.33	2	0.17	6.33	0.83	2015	5.5	36	NA
1.83	101	776	20155.5	0.17	7.16	2	0.17	7.16	1.66	2015	5.5	0	0
2	102	777	20155.5	0.17	7.33	2	0.17	7.33	1.83	2015	5.5	20	NA
3	103	778	20155.5	0.17	8.33	2	0.17	8.33	2.83	2015	5.5	24	NA
3.67	104	779	20155.5	0.17	9	2	0.17	9.00	3.50	2015	5.5	0	0
3.84	105	780	20155.5	0.17	9.17	2	0.17	9.17	3.67	2015	5.5	74	NA
4.17	106	781	20155.5	0.17	9.5	2	0.17	9.50	4.00	2015	5.5	24	NA
4.75	107	782	20155.5	0.17	10.08	2	0.17	10.08	4.58	2015	5.5	16	NA
1.83	108	783	20155.5	1	6.33	3	1.00	6.33	1.66	2015	5.5	0	0
2	109	784	20155.5	1	6.5	3	1.00	6.50	1.83	2015	5.5	20	NA
3	110	785	20155.5	1	7.5	3	1.00	7.50	2.83	2015	5.5	24	NA
3.67	111	786	20155.5	1	8.17	3	1.00	8.17	3.50	2015	5.5	0	0
3.84	112	787	20155.5	1	8.34	3	1.00	8.34	3.67	2015	5.5	74	NA
4.17	113	788	20155.5	1	8.67	3	1.00	8.67	4.00	2015	5.5	24	NA
4.75	114	789	20155.5	1	9.25	3	1.00	9.25	4.58	2015	5.5	16	NA
2	115	790	20155.5	1.83	5.67	4	1.83	5.67	1.83	2015	5.5	20	NA
3	116	791	20155.5	1.83	6.67	4	1.83	6.67	2.83	2015	5.5	24	NA
3.67	117	792	20155.5	1.83	7.34	4	1.83	7.34	3.50	2015	5.5	0	0
3.84	118	793	20155.5	1.83	7.51	4	1.83	7.51	3.67	2015	5.5	74	NA
4.17	119	794	20155.5	1.83	7.84	4	1.83	7.84	4.00	2015	5.5	24	NA
4.75	120	795	20155.5	1.83	8.42	4	1.83	8.42	4.58	2015	5.5	16	NA
3	121	796	20155.5	2	6.5	5	2.00	6.50	2.83	2015	5.5	24	NA
3.67	122	797	20155.5	2	7.17	5	2.00	7.17	3.50	2015	5.5	0	0
3.84	123	798	20155.5	2	7.34	5	2.00	7.34	3.67	2015	5.5	74	NA
4.17	124	799	20155.5	2	7.67	5	2.00	7.67	4.00	2015	5.5	24	NA
4.75	125	800	20155.5	2	8.25	5	2.00	8.25	4.58	2015	5.5	16	NA
3.67	126	801	20155.5	3	6.17	6	3.00	6.17	3.50	2015	5.5	0	0
3.84	127	802	20155.5	3	6.34	6	3.00	6.34	3.67	2015	5.5	74	NA
4.17	128	803	20155.5	3	6.67	6	3.00	6.67	4.00	2015	5.5	24	NA
4.75	129	804	20155.5	3	7.25	6	3.00	7.25	4.58	2015	5.5	16	NA
3.84	130	805	20155.5	3.67	5.67	7	3.67	5.67	3.67	2015	5.5	74	NA
4.17	131	806	20155.5	3.67	6	7	3.67	6.00	4.00	2015	5.5	24	NA
4.75	132	807	20155.5	3.67	6.58	7	3.67	6.58	4.58	2015	5.5	16	NA
4.17	133	808	20155.5	3.84	5.83	8	3.84	5.83	4.00	2015	5.5	24	NA
4.75	134	809	20155.5	3.84	6.41	8	3.84	6.41	4.58	2015	5.5	16	NA
4.75	135	810	20155.5	4.17	6.08	9	4.17	6.08	4.58	2015	5.5	16	NA
0.17	136	811	20175.5	0	5.67	1	0.00	5.67	0.00	2017	5.5	24	NA
1	137	812	20175.5	0	6.5	1	0.00	6.50	0.83	2017	5.5	36	NA
1.83	138	813	20175.5	0	7.33	1	0.00	7.33	1.66	2017	5.5	0	NA
2	139	814	20175.5	0	7.5	1	0.00	7.50	1.83	2017	5.5	20	NA
3	140	815	20175.5	0	8.5	1	0.00	8.50	2.83	2017	5.5	24	NA
3.67	141	816	20175.5	0	9.17	1	0.00	9.17	3.50	2017	5.5	0	0
3.84	142	817	20175.5	0	9.34	1	0.00	9.34	3.67	2017	5.5	74	NA
4.17	143	818	20175.5	0	9.67	1	0.00	9.67	4.00	2017	5.5	24	NA
4.75	144	819	20175.5	0	10.25	1	0.00	10.25	4.58	2017	5.5	16	NA
1	145	820	20175.5	0.17	6.33	2	0.17	6.33	0.83	2017	5.5	36	NA
1.83	146	821	20175.5	0.17	7.16	2	0.17	7.16	1.66	2017	5.5	0	NA
2	147	822	20175.5	0.17	7.33	2	0.17	7.33	1.83	2017	5.5	20	NA
3	148	823	20175.5	0.17	8.33	2	0.17	8.33	2.83	2017	5.5	24	NA
3.67	149	824	20175.5	0.17	9	2	0.17	9.00	3.50	2017	5.5	0	0
3.84	150	825	20175.5	0.17	9.17	2	0.17	9.17	3.67	2017	5.5	74	NA
4.17	151	826	20175.5	0.17	9.5	2	0.17	9.50	4.00	2017	5.5	24	NA
4.75	152	827	20175.5	0.17	10.08	2	0.17	10.08	4.58	2017	5.5	16	NA
1.83	153	828	20175.5	1	6.33	3	1.00	6.33	1.66	2017	5.5	0	NA
2	154	829	20175.5	1	6.5	3	1.00	6.50	1.83	2017	5.5	20	NA
3	155	830	20175.5	1	7.5	3	1.00	7.50	2.83	2017	5.5	24	NA
3.67	156	831	20175.5	1	8.17	3	1.00	8.17	3.50	2017	5.5	0	0
3.84	157	832	20175.5	1	8.34	3	1.00	8.34	3.67	2017	5.5	74	NA
4.17	158	833	20175.5	1	8.67	3	1.00	8.67	4.00	2017	5.5	24	NA
4.75	159	834	20175.5	1	9.25	3	1.00	9.25	4.58	2017	5.5	16	NA
2	160	835	20175.5	1.83	5.67	4	1.83	5.67	1.83	2017	5.5	20	NA
3	161	836	20175.5	1.83	6.67	4	1.83	6.67	2.83	2017	5.5	24	NA
3.67	162	837	20175.5	1.83	7.34	4	1.83	7.34	3.50	2017	5.5	0	0
3.84	163	838	20175.5	1.83	7.51	4	1.83	7.51	3.67	2017	5.5	74	NA
4.17	164	839	20175.5	1.83	7.84	4	1.83	7.84	4.00	2017	5.5	24	NA
4.75	165	840	20175.5	1.83	8.42	4	1.83	8.42	4.58	2017	5.5	16	NA
3	166	841	20175.5	2	6.5	5	2.00	6.50	2.83	2017	5.5	24	NA
3.67	167	842	20175.5	2	7.17	5	2.00	7.17	3.50	2017	5.5	0	0
3.84	168	843	20175.5	2	7.34	5	2.00	7.34	3.67	2017	5.5	74	NA
4.17	169	844	20175.5	2	7.67	5	2.00	7.67	4.00	2017	5.5	24	NA
4.75	170	845	20175.5	2	8.25	5	2.00	8.25	4.58	2017	5.5	16	NA
3.67	171	846	20175.5	3	6.17	6	3.00	6.17	3.50	2017	5.5	0	0
3.84	172	847	20175.5	3	6.34	6	3.00	6.34	3.67	2017	5.5	74	NA
4.17	173	848	20175.5	3	6.67	6	3.00	6.67	4.00	2017	5.5	24	NA
4.75	174	849	20175.5	3	7.25	6	3.00	7.25	4.58	2017	5.5	16	NA
3.84	175	850	20175.5	3.67	5.67	7	3.67	5.67	3.67	2017	5.5	74	NA
4.17	176	851	20175.5	3.67	6	7	3.67	6.00	4.00	2017	5.5	24	NA
4.75	177	852	20175.5	3.67	6.58	7	3.67	6.58	4.58	2017	5.5	16	NA
4.17	178	853	20175.5	3.84	5.83	8	3.84	5.83	4.00	2017	5.5	24	NA
4.75	179	854	20175.5	3.84	6.41	8	3.84	6.41	4.58	2017	5.5	16	NA
4.75	180	855	20175.5	4.17	6.08	9	4.17	6.08	4.58	2017	5.5	16	NA
0.17	181	856	20195.5	0	5.67	1	0.00	5.67	0.00	2019	5.5	24	NA
1	182	857	20195.5	0	6.5	1	0.00	6.50	0.83	2019	5.5	36	NA
1.83	183	858	20195.5	0	7.33	1	0.00	7.33	1.66	2019	5.5	0	NA
2	184	859	20195.5	0	7.5	1	0.00	7.50	1.83	2019	5.5	20	NA
3	185	860	20195.5	0	8.5	1	0.00	8.50	2.83	2019	5.5	24	NA
3.67	186	861	20195.5	0	9.17	1	0.00	9.17	3.50	2019	5.5	0	NA
3.84	187	862	20195.5	0	9.34	1	0.00	9.34	3.67	2019	5.5	74	NA
4.17	188	863	20195.5	0	9.67	1	0.00	9.67	4.00	2019	5.5	24	NA
4.75	189	864	20195.5	0	10.25	1	0.00	10.25	4.58	2019	5.5	16	NA
1	190	865	20195.5	0.17	6.33	2	0.17	6.33	0.83	2019	5.5	36	NA
1.83	191	866	20195.5	0.17	7.16	2	0.17	7.16	1.66	2019	5.5	0	NA
2	192	867	20195.5	0.17	7.33	2	0.17	7.33	1.83	2019	5.5	20	NA
3	193	868	20195.5	0.17	8.33	2	0.17	8.33	2.83	2019	5.5	24	NA
3.67	194	869	20195.5	0.17	9	2	0.17	9.00	3.50	2019	5.5	0	NA
3.84	195	870	20195.5	0.17	9.17	2	0.17	9.17	3.67	2019	5.5	74	NA
4.17	196	871	20195.5	0.17	9.5	2	0.17	9.50	4.00	2019	5.5	24	NA
4.75	197	872	20195.5	0.17	10.08	2	0.17	10.08	4.58	2019	5.5	16	NA
1.83	198	873	20195.5	1	6.33	3	1.00	6.33	1.66	2019	5.5	0	NA
2	199	874	20195.5	1	6.5	3	1.00	6.50	1.83	2019	5.5	20	NA
3	200	875	20195.5	1	7.5	3	1.00	7.50	2.83	2019	5.5	24	NA
3.67	201	876	20195.5	1	8.17	3	1.00	8.17	3.50	2019	5.5	0	NA
3.84	202	877	20195.5	1	8.34	3	1.00	8.34	3.67	2019	5.5	74	NA
4.17	203	878	20195.5	1	8.67	3	1.00	8.67	4.00	2019	5.5	24	NA
4.75	204	879	20195.5	1	9.25	3	1.00	9.25	4.58	2019	5.5	16	NA
2	205	880	20195.5	1.83	5.67	4	1.83	5.67	1.83	2019	5.5	20	NA
3	206	881	20195.5	1.83	6.67	4	1.83	6.67	2.83	2019	5.5	24	NA
3.67	207	882	20195.5	1.83	7.34	4	1.83	7.34	3.50	2019	5.5	0	NA
3.84	208	883	20195.5	1.83	7.51	4	1.83	7.51	3.67	2019	5.5	74	NA
4.17	209	884	20195.5	1.83	7.84	4	1.83	7.84	4.00	2019	5.5	24	NA
4.75	210	885	20195.5	1.83	8.42	4	1.83	8.42	4.58	2019	5.5	16	NA
3	211	886	20195.5	2	6.5	5	2.00	6.50	2.83	2019	5.5	24	NA
3.67	212	887	20195.5	2	7.17	5	2.00	7.17	3.50	2019	5.5	0	NA
3.84	213	888	20195.5	2	7.34	5	2.00	7.34	3.67	2019	5.5	74	NA
4.17	214	889	20195.5	2	7.67	5	2.00	7.67	4.00	2019	5.5	24	NA
4.75	215	890	20195.5	2	8.25	5	2.00	8.25	4.58	2019	5.5	16	NA
3.67	216	891	20195.5	3	6.17	6	3.00	6.17	3.50	2019	5.5	0	NA
3.84	217	892	20195.5	3	6.34	6	3.00	6.34	3.67	2019	5.5	74	NA
4.17	218	893	20195.5	3	6.67	6	3.00	6.67	4.00	2019	5.5	24	NA
4.75	219	894	20195.5	3	7.25	6	3.00	7.25	4.58	2019	5.5	16	NA
3.84	220	895	20195.5	3.67	5.67	7	3.67	5.67	3.67	2019	5.5	74	NA
4.17	221	896	20195.5	3.67	6	7	3.67	6.00	4.00	2019	5.5	24	NA
4.75	222	897	20195.5	3.67	6.58	7	3.67	6.58	4.58	2019	5.5	16	NA
4.17	223	898	20195.5	3.84	5.83	8	3.84	5.83	4.00	2019	5.5	24	NA
4.75	224	899	20195.5	3.84	6.41	8	3.84	6.41	4.58	2019	5.5	16	NA
4.75	225	900	20195.5	4.17	6.08	9	4.17	6.08	4.58	2019	5.5	16	NA
0.17	226	901	20156.5	0	6.67	1	0.00	6.67	0.00	2015	6.5	24	NA
1	227	902	20156.5	0	7.5	1	0.00	7.50	0.83	2015	6.5	36	NA
1.83	228	903	20156.5	0	8.33	1	0.00	8.33	1.66	2015	6.5	0	0
2	229	904	20156.5	0	8.5	1	0.00	8.50	1.83	2015	6.5	20	NA
3	230	905	20156.5	0	9.5	1	0.00	9.50	2.83	2015	6.5	24	NA
3.67	231	906	20156.5	0	10.17	1	0.00	10.17	3.50	2015	6.5	0	0
3.84	232	907	20156.5	0	10.34	1	0.00	10.34	3.67	2015	6.5	74	NA
4.17	233	908	20156.5	0	10.67	1	0.00	10.67	4.00	2015	6.5	24	NA
4.75	234	909	20156.5	0	11.25	1	0.00	11.25	4.58	2015	6.5	16	NA
1	235	910	20156.5	0.17	7.33	2	0.17	7.33	0.83	2015	6.5	36	NA
1.83	236	911	20156.5	0.17	8.16	2	0.17	8.16	1.66	2015	6.5	0	0
2	237	912	20156.5	0.17	8.33	2	0.17	8.33	1.83	2015	6.5	20	NA
3	238	913	20156.5	0.17	9.33	2	0.17	9.33	2.83	2015	6.5	24	NA
3.67	239	914	20156.5	0.17	10	2	0.17	10.00	3.50	2015	6.5	0	0
3.84	240	915	20156.5	0.17	10.17	2	0.17	10.17	3.67	2015	6.5	74	NA
4.17	241	916	20156.5	0.17	10.5	2	0.17	10.50	4.00	2015	6.5	24	NA
4.75	242	917	20156.5	0.17	11.08	2	0.17	11.08	4.58	2015	6.5	16	NA
1.83	243	918	20156.5	1	7.33	3	1.00	7.33	1.66	2015	6.5	0	0
2	244	919	20156.5	1	7.5	3	1.00	7.50	1.83	2015	6.5	20	NA
3	245	920	20156.5	1	8.5	3	1.00	8.50	2.83	2015	6.5	24	NA
3.67	246	921	20156.5	1	9.17	3	1.00	9.17	3.50	2015	6.5	0	0
3.84	247	922	20156.5	1	9.34	3	1.00	9.34	3.67	2015	6.5	74	NA
4.17	248	923	20156.5	1	9.67	3	1.00	9.67	4.00	2015	6.5	24	NA
4.75	249	924	20156.5	1	10.25	3	1.00	10.25	4.58	2015	6.5	16	NA
2	250	925	20156.5	1.83	6.67	4	1.83	6.67	1.83	2015	6.5	20	NA
3	251	926	20156.5	1.83	7.67	4	1.83	7.67	2.83	2015	6.5	24	NA
3.67	252	927	20156.5	1.83	8.34	4	1.83	8.34	3.50	2015	6.5	0	0
3.84	253	928	20156.5	1.83	8.51	4	1.83	8.51	3.67	2015	6.5	74	NA
4.17	254	929	20156.5	1.83	8.84	4	1.83	8.84	4.00	2015	6.5	24	NA
4.75	255	930	20156.5	1.83	9.42	4	1.83	9.42	4.58	2015	6.5	16	NA
3	256	931	20156.5	2	7.5	5	2.00	7.50	2.83	2015	6.5	24	NA
3.67	257	932	20156.5	2	8.17	5	2.00	8.17	3.50	2015	6.5	0	0
3.84	258	933	20156.5	2	8.34	5	2.00	8.34	3.67	2015	6.5	74	NA
4.17	259	934	20156.5	2	8.67	5	2.00	8.67	4.00	2015	6.5	24	NA
4.75	260	935	20156.5	2	9.25	5	2.00	9.25	4.58	2015	6.5	16	NA
3.67	261	936	20156.5	3	7.17	6	3.00	7.17	3.50	2015	6.5	0	0
3.84	262	937	20156.5	3	7.34	6	3.00	7.34	3.67	2015	6.5	74	NA
4.17	263	938	20156.5	3	7.67	6	3.00	7.67	4.00	2015	6.5	24	NA
4.75	264	939	20156.5	3	8.25	6	3.00	8.25	4.58	2015	6.5	16	NA
3.84	265	940	20156.5	3.67	6.67	7	3.67	6.67	3.67	2015	6.5	74	NA
4.17	266	941	20156.5	3.67	7	7	3.67	7.00	4.00	2015	6.5	24	NA
4.75	267	942	20156.5	3.67	7.58	7	3.67	7.58	4.58	2015	6.5	16	NA
4.17	268	943	20156.5	3.84	6.83	8	3.84	6.83	4.00	2015	6.5	24	NA
4.75	269	944	20156.5	3.84	7.41	8	3.84	7.41	4.58	2015	6.5	16	NA
4.75	270	945	20156.5	4.17	7.08	9	4.17	7.08	4.58	2015	6.5	16	NA
0.17	271	946	20176.5	0	6.67	1	0.00	6.67	0.00	2017	6.5	24	NA
1	272	947	20176.5	0	7.5	1	0.00	7.50	0.83	2017	6.5	36	NA
1.83	273	948	20176.5	0	8.33	1	0.00	8.33	1.66	2017	6.5	0	NA
2	274	949	20176.5	0	8.5	1	0.00	8.50	1.83	2017	6.5	20	NA
3	275	950	20176.5	0	9.5	1	0.00	9.50	2.83	2017	6.5	24	NA
3.67	276	951	20176.5	0	10.17	1	0.00	10.17	3.50	2017	6.5	0	0
3.84	277	952	20176.5	0	10.34	1	0.00	10.34	3.67	2017	6.5	74	NA
4.17	278	953	20176.5	0	10.67	1	0.00	10.67	4.00	2017	6.5	24	NA
4.75	279	954	20176.5	0	11.25	1	0.00	11.25	4.58	2017	6.5	16	NA
1	280	955	20176.5	0.17	7.33	2	0.17	7.33	0.83	2017	6.5	36	NA
1.83	281	956	20176.5	0.17	8.16	2	0.17	8.16	1.66	2017	6.5	0	NA
2	282	957	20176.5	0.17	8.33	2	0.17	8.33	1.83	2017	6.5	20	NA
3	283	958	20176.5	0.17	9.33	2	0.17	9.33	2.83	2017	6.5	24	NA
3.67	284	959	20176.5	0.17	10	2	0.17	10.00	3.50	2017	6.5	0	0
3.84	285	960	20176.5	0.17	10.17	2	0.17	10.17	3.67	2017	6.5	74	NA
4.17	286	961	20176.5	0.17	10.5	2	0.17	10.50	4.00	2017	6.5	24	NA
4.75	287	962	20176.5	0.17	11.08	2	0.17	11.08	4.58	2017	6.5	16	NA
1.83	288	963	20176.5	1	7.33	3	1.00	7.33	1.66	2017	6.5	0	NA
2	289	964	20176.5	1	7.5	3	1.00	7.50	1.83	2017	6.5	20	NA
3	290	965	20176.5	1	8.5	3	1.00	8.50	2.83	2017	6.5	24	NA
3.67	291	966	20176.5	1	9.17	3	1.00	9.17	3.50	2017	6.5	0	0
3.84	292	967	20176.5	1	9.34	3	1.00	9.34	3.67	2017	6.5	74	NA
4.17	293	968	20176.5	1	9.67	3	1.00	9.67	4.00	2017	6.5	24	NA
4.75	294	969	20176.5	1	10.25	3	1.00	10.25	4.58	2017	6.5	16	NA
2	295	970	20176.5	1.83	6.67	4	1.83	6.67	1.83	2017	6.5	20	NA
3	296	971	20176.5	1.83	7.67	4	1.83	7.67	2.83	2017	6.5	24	NA
3.67	297	972	20176.5	1.83	8.34	4	1.83	8.34	3.50	2017	6.5	0	0
3.84	298	973	20176.5	1.83	8.51	4	1.83	8.51	3.67	2017	6.5	74	NA
4.17	299	974	20176.5	1.83	8.84	4	1.83	8.84	4.00	2017	6.5	24	NA
4.75	300	975	20176.5	1.83	9.42	4	1.83	9.42	4.58	2017	6.5	16	NA
3	301	976	20176.5	2	7.5	5	2.00	7.50	2.83	2017	6.5	24	NA
3.67	302	977	20176.5	2	8.17	5	2.00	8.17	3.50	2017	6.5	0	0
3.84	303	978	20176.5	2	8.34	5	2.00	8.34	3.67	2017	6.5	74	NA
4.17	304	979	20176.5	2	8.67	5	2.00	8.67	4.00	2017	6.5	24	NA
4.75	305	980	20176.5	2	9.25	5	2.00	9.25	4.58	2017	6.5	16	NA
3.67	306	981	20176.5	3	7.17	6	3.00	7.17	3.50	2017	6.5	0	0
3.84	307	982	20176.5	3	7.34	6	3.00	7.34	3.67	2017	6.5	74	NA
4.17	308	983	20176.5	3	7.67	6	3.00	7.67	4.00	2017	6.5	24	NA
4.75	309	984	20176.5	3	8.25	6	3.00	8.25	4.58	2017	6.5	16	NA
3.84	310	985	20176.5	3.67	6.67	7	3.67	6.67	3.67	2017	6.5	74	NA
4.17	311	986	20176.5	3.67	7	7	3.67	7.00	4.00	2017	6.5	24	NA
4.75	312	987	20176.5	3.67	7.58	7	3.67	7.58	4.58	2017	6.5	16	NA
4.17	313	988	20176.5	3.84	6.83	8	3.84	6.83	4.00	2017	6.5	24	NA
4.75	314	989	20176.5	3.84	7.41	8	3.84	7.41	4.58	2017	6.5	16	NA
4.75	315	990	20176.5	4.17	7.08	9	4.17	7.08	4.58	2017	6.5	16	NA
0.17	316	991	20196.5	0	6.67	1	0.00	6.67	0.00	2019	6.5	24	NA
1	317	992	20196.5	0	7.5	1	0.00	7.50	0.83	2019	6.5	36	NA
1.83	318	993	20196.5	0	8.33	1	0.00	8.33	1.66	2019	6.5	0	NA
2	319	994	20196.5	0	8.5	1	0.00	8.50	1.83	2019	6.5	20	NA
3	320	995	20196.5	0	9.5	1	0.00	9.50	2.83	2019	6.5	24	NA
3.67	321	996	20196.5	0	10.17	1	0.00	10.17	3.50	2019	6.5	0	NA
3.84	322	997	20196.5	0	10.34	1	0.00	10.34	3.67	2019	6.5	74	NA
4.17	323	998	20196.5	0	10.67	1	0.00	10.67	4.00	2019	6.5	24	NA
4.75	324	999	20196.5	0	11.25	1	0.00	11.25	4.58	2019	6.5	16	NA
1	325	1000	20196.5	0.17	7.33	2	0.17	7.33	0.83	2019	6.5	36	NA
1.83	326	1001	20196.5	0.17	8.16	2	0.17	8.16	1.66	2019	6.5	0	NA
2	327	1002	20196.5	0.17	8.33	2	0.17	8.33	1.83	2019	6.5	20	NA
3	328	1003	20196.5	0.17	9.33	2	0.17	9.33	2.83	2019	6.5	24	NA
3.67	329	1004	20196.5	0.17	10	2	0.17	10.00	3.50	2019	6.5	0	NA
3.84	330	1005	20196.5	0.17	10.17	2	0.17	10.17	3.67	2019	6.5	74	NA
4.17	331	1006	20196.5	0.17	10.5	2	0.17	10.50	4.00	2019	6.5	24	NA
4.75	332	1007	20196.5	0.17	11.08	2	0.17	11.08	4.58	2019	6.5	16	NA
1.83	333	1008	20196.5	1	7.33	3	1.00	7.33	1.66	2019	6.5	0	NA
2	334	1009	20196.5	1	7.5	3	1.00	7.50	1.83	2019	6.5	20	NA
3	335	1010	20196.5	1	8.5	3	1.00	8.50	2.83	2019	6.5	24	NA
3.67	336	1011	20196.5	1	9.17	3	1.00	9.17	3.50	2019	6.5	0	NA
3.84	337	1012	20196.5	1	9.34	3	1.00	9.34	3.67	2019	6.5	74	NA
4.17	338	1013	20196.5	1	9.67	3	1.00	9.67	4.00	2019	6.5	24	NA
4.75	339	1014	20196.5	1	10.25	3	1.00	10.25	4.58	2019	6.5	16	NA
2	340	1015	20196.5	1.83	6.67	4	1.83	6.67	1.83	2019	6.5	20	NA
3	341	1016	20196.5	1.83	7.67	4	1.83	7.67	2.83	2019	6.5	24	NA
3.67	342	1017	20196.5	1.83	8.34	4	1.83	8.34	3.50	2019	6.5	0	NA
3.84	343	1018	20196.5	1.83	8.51	4	1.83	8.51	3.67	2019	6.5	74	NA
4.17	344	1019	20196.5	1.83	8.84	4	1.83	8.84	4.00	2019	6.5	24	NA
4.75	345	1020	20196.5	1.83	9.42	4	1.83	9.42	4.58	2019	6.5	16	NA
3	346	1021	20196.5	2	7.5	5	2.00	7.50	2.83	2019	6.5	24	NA
3.67	347	1022	20196.5	2	8.17	5	2.00	8.17	3.50	2019	6.5	0	NA
3.84	348	1023	20196.5	2	8.34	5	2.00	8.34	3.67	2019	6.5	74	NA
4.17	349	1024	20196.5	2	8.67	5	2.00	8.67	4.00	2019	6.5	24	NA
4.75	350	1025	20196.5	2	9.25	5	2.00	9.25	4.58	2019	6.5	16	NA
3.67	351	1026	20196.5	3	7.17	6	3.00	7.17	3.50	2019	6.5	0	NA
3.84	352	1027	20196.5	3	7.34	6	3.00	7.34	3.67	2019	6.5	74	NA
4.17	353	1028	20196.5	3	7.67	6	3.00	7.67	4.00	2019	6.5	24	NA
4.75	354	1029	20196.5	3	8.25	6	3.00	8.25	4.58	2019	6.5	16	NA
3.84	355	1030	20196.5	3.67	6.67	7	3.67	6.67	3.67	2019	6.5	74	NA
4.17	356	1031	20196.5	3.67	7	7	3.67	7.00	4.00	2019	6.5	24	NA
4.75	357	1032	20196.5	3.67	7.58	7	3.67	7.58	4.58	2019	6.5	16	NA
4.17	358	1033	20196.5	3.84	6.83	8	3.84	6.83	4.00	2019	6.5	24	NA
4.75	359	1034	20196.5	3.84	7.41	8	3.84	7.41	4.58	2019	6.5	16	NA
4.75	360	1035	20196.5	4.17	7.08	9	4.17	7.08	4.58	2019	6.5	16	NA
0.17	361	1036	20157.5	0	7.67	1	0.00	7.67	0.00	2015	7.5	24	NA
1	362	1037	20157.5	0	8.5	1	0.00	8.50	0.83	2015	7.5	36	NA
1.83	363	1038	20157.5	0	9.33	1	0.00	9.33	1.66	2015	7.5	0	0
2	364	1039	20157.5	0	9.5	1	0.00	9.50	1.83	2015	7.5	20	NA
3	365	1040	20157.5	0	10.5	1	0.00	10.50	2.83	2015	7.5	24	NA
3.67	366	1041	20157.5	0	11.17	1	0.00	11.17	3.50	2015	7.5	0	0
3.84	367	1042	20157.5	0	11.34	1	0.00	11.34	3.67	2015	7.5	74	NA
4.17	368	1043	20157.5	0	11.67	1	0.00	11.67	4.00	2015	7.5	24	NA
4.75	369	1044	20157.5	0	12.25	1	0.00	12.25	4.58	2015	7.5	16	NA
1	370	1045	20157.5	0.17	8.33	2	0.17	8.33	0.83	2015	7.5	36	NA
1.83	371	1046	20157.5	0.17	9.16	2	0.17	9.16	1.66	2015	7.5	0	0
2	372	1047	20157.5	0.17	9.33	2	0.17	9.33	1.83	2015	7.5	20	NA
3	373	1048	20157.5	0.17	10.33	2	0.17	10.33	2.83	2015	7.5	24	NA
3.67	374	1049	20157.5	0.17	11	2	0.17	11.00	3.50	2015	7.5	0	0
3.84	375	1050	20157.5	0.17	11.17	2	0.17	11.17	3.67	2015	7.5	74	NA
4.17	376	1051	20157.5	0.17	11.5	2	0.17	11.50	4.00	2015	7.5	24	NA
4.75	377	1052	20157.5	0.17	12.08	2	0.17	12.08	4.58	2015	7.5	16	NA
1.83	378	1053	20157.5	1	8.33	3	1.00	8.33	1.66	2015	7.5	0	0
2	379	1054	20157.5	1	8.5	3	1.00	8.50	1.83	2015	7.5	20	NA
3	380	1055	20157.5	1	9.5	3	1.00	9.50	2.83	2015	7.5	24	NA
3.67	381	1056	20157.5	1	10.17	3	1.00	10.17	3.50	2015	7.5	0	0
3.84	382	1057	20157.5	1	10.34	3	1.00	10.34	3.67	2015	7.5	74	NA
4.17	383	1058	20157.5	1	10.67	3	1.00	10.67	4.00	2015	7.5	24	NA
4.75	384	1059	20157.5	1	11.25	3	1.00	11.25	4.58	2015	7.5	16	NA
2	385	1060	20157.5	1.83	7.67	4	1.83	7.67	1.83	2015	7.5	20	NA
3	386	1061	20157.5	1.83	8.67	4	1.83	8.67	2.83	2015	7.5	24	NA
3.67	387	1062	20157.5	1.83	9.34	4	1.83	9.34	3.50	2015	7.5	0	0
3.84	388	1063	20157.5	1.83	9.51	4	1.83	9.51	3.67	2015	7.5	74	NA
4.17	389	1064	20157.5	1.83	9.84	4	1.83	9.84	4.00	2015	7.5	24	NA
4.75	390	1065	20157.5	1.83	10.42	4	1.83	10.42	4.58	2015	7.5	16	NA
3	391	1066	20157.5	2	8.5	5	2.00	8.50	2.83	2015	7.5	24	NA
3.67	392	1067	20157.5	2	9.17	5	2.00	9.17	3.50	2015	7.5	0	0
3.84	393	1068	20157.5	2	9.34	5	2.00	9.34	3.67	2015	7.5	74	NA
4.17	394	1069	20157.5	2	9.67	5	2.00	9.67	4.00	2015	7.5	24	NA
4.75	395	1070	20157.5	2	10.25	5	2.00	10.25	4.58	2015	7.5	16	NA
3.67	396	1071	20157.5	3	8.17	6	3.00	8.17	3.50	2015	7.5	0	0
3.84	397	1072	20157.5	3	8.34	6	3.00	8.34	3.67	2015	7.5	74	NA
4.17	398	1073	20157.5	3	8.67	6	3.00	8.67	4.00	2015	7.5	24	NA
4.75	399	1074	20157.5	3	9.25	6	3.00	9.25	4.58	2015	7.5	16	NA
3.84	400	1075	20157.5	3.67	7.67	7	3.67	7.67	3.67	2015	7.5	74	NA
4.17	401	1076	20157.5	3.67	8	7	3.67	8.00	4.00	2015	7.5	24	NA
4.75	402	1077	20157.5	3.67	8.58	7	3.67	8.58	4.58	2015	7.5	16	NA
4.17	403	1078	20157.5	3.84	7.83	8	3.84	7.83	4.00	2015	7.5	24	NA
4.75	404	1079	20157.5	3.84	8.41	8	3.84	8.41	4.58	2015	7.5	16	NA
4.75	405	1080	20157.5	4.17	8.08	9	4.17	8.08	4.58	2015	7.5	16	NA
0.17	406	1081	20177.5	0	7.67	1	0.00	7.67	0.00	2017	7.5	24	NA
1	407	1082	20177.5	0	8.5	1	0.00	8.50	0.83	2017	7.5	36	NA
1.83	408	1083	20177.5	0	9.33	1	0.00	9.33	1.66	2017	7.5	0	NA
2	409	1084	20177.5	0	9.5	1	0.00	9.50	1.83	2017	7.5	20	NA
3	410	1085	20177.5	0	10.5	1	0.00	10.50	2.83	2017	7.5	24	NA
3.67	411	1086	20177.5	0	11.17	1	0.00	11.17	3.50	2017	7.5	0	0
3.84	412	1087	20177.5	0	11.34	1	0.00	11.34	3.67	2017	7.5	74	NA
4.17	413	1088	20177.5	0	11.67	1	0.00	11.67	4.00	2017	7.5	24	NA
4.75	414	1089	20177.5	0	12.25	1	0.00	12.25	4.58	2017	7.5	16	NA
1	415	1090	20177.5	0.17	8.33	2	0.17	8.33	0.83	2017	7.5	36	NA
1.83	416	1091	20177.5	0.17	9.16	2	0.17	9.16	1.66	2017	7.5	0	NA
2	417	1092	20177.5	0.17	9.33	2	0.17	9.33	1.83	2017	7.5	20	NA
3	418	1093	20177.5	0.17	10.33	2	0.17	10.33	2.83	2017	7.5	24	NA
3.67	419	1094	20177.5	0.17	11	2	0.17	11.00	3.50	2017	7.5	0	0
3.84	420	1095	20177.5	0.17	11.17	2	0.17	11.17	3.67	2017	7.5	74	NA
4.17	421	1096	20177.5	0.17	11.5	2	0.17	11.50	4.00	2017	7.5	24	NA
4.75	422	1097	20177.5	0.17	12.08	2	0.17	12.08	4.58	2017	7.5	16	NA
1.83	423	1098	20177.5	1	8.33	3	1.00	8.33	1.66	2017	7.5	0	NA
2	424	1099	20177.5	1	8.5	3	1.00	8.50	1.83	2017	7.5	20	NA
3	425	1100	20177.5	1	9.5	3	1.00	9.50	2.83	2017	7.5	24	NA
3.67	426	1101	20177.5	1	10.17	3	1.00	10.17	3.50	2017	7.5	0	0
3.84	427	1102	20177.5	1	10.34	3	1.00	10.34	3.67	2017	7.5	74	NA
4.17	428	1103	20177.5	1	10.67	3	1.00	10.67	4.00	2017	7.5	24	NA
4.75	429	1104	20177.5	1	11.25	3	1.00	11.25	4.58	2017	7.5	16	NA
2	430	1105	20177.5	1.83	7.67	4	1.83	7.67	1.83	2017	7.5	20	NA
3	431	1106	20177.5	1.83	8.67	4	1.83	8.67	2.83	2017	7.5	24	NA
3.67	432	1107	20177.5	1.83	9.34	4	1.83	9.34	3.50	2017	7.5	0	0
3.84	433	1108	20177.5	1.83	9.51	4	1.83	9.51	3.67	2017	7.5	74	NA
4.17	434	1109	20177.5	1.83	9.84	4	1.83	9.84	4.00	2017	7.5	24	NA
4.75	435	1110	20177.5	1.83	10.42	4	1.83	10.42	4.58	2017	7.5	16	NA
3	436	1111	20177.5	2	8.5	5	2.00	8.50	2.83	2017	7.5	24	NA
3.67	437	1112	20177.5	2	9.17	5	2.00	9.17	3.50	2017	7.5	0	0
3.84	438	1113	20177.5	2	9.34	5	2.00	9.34	3.67	2017	7.5	74	NA
4.17	439	1114	20177.5	2	9.67	5	2.00	9.67	4.00	2017	7.5	24	NA
4.75	440	1115	20177.5	2	10.25	5	2.00	10.25	4.58	2017	7.5	16	NA
3.67	441	1116	20177.5	3	8.17	6	3.00	8.17	3.50	2017	7.5	0	0
3.84	442	1117	20177.5	3	8.34	6	3.00	8.34	3.67	2017	7.5	74	NA
4.17	443	1118	20177.5	3	8.67	6	3.00	8.67	4.00	2017	7.5	24	NA
4.75	444	1119	20177.5	3	9.25	6	3.00	9.25	4.58	2017	7.5	16	NA
3.84	445	1120	20177.5	3.67	7.67	7	3.67	7.67	3.67	2017	7.5	74	NA
4.17	446	1121	20177.5	3.67	8	7	3.67	8.00	4.00	2017	7.5	24	NA
4.75	447	1122	20177.5	3.67	8.58	7	3.67	8.58	4.58	2017	7.5	16	NA
4.17	448	1123	20177.5	3.84	7.83	8	3.84	7.83	4.00	2017	7.5	24	NA
4.75	449	1124	20177.5	3.84	8.41	8	3.84	8.41	4.58	2017	7.5	16	NA
4.75	450	1125	20177.5	4.17	8.08	9	4.17	8.08	4.58	2017	7.5	16	NA
0.17	451	1126	20197.5	0	7.67	1	0.00	7.67	0.00	2019	7.5	24	NA
1	452	1127	20197.5	0	8.5	1	0.00	8.50	0.83	2019	7.5	36	NA
1.83	453	1128	20197.5	0	9.33	1	0.00	9.33	1.66	2019	7.5	0	NA
2	454	1129	20197.5	0	9.5	1	0.00	9.50	1.83	2019	7.5	20	NA
3	455	1130	20197.5	0	10.5	1	0.00	10.50	2.83	2019	7.5	24	NA
3.67	456	1131	20197.5	0	11.17	1	0.00	11.17	3.50	2019	7.5	0	NA
3.84	457	1132	20197.5	0	11.34	1	0.00	11.34	3.67	2019	7.5	74	NA
4.17	458	1133	20197.5	0	11.67	1	0.00	11.67	4.00	2019	7.5	24	NA
4.75	459	1134	20197.5	0	12.25	1	0.00	12.25	4.58	2019	7.5	16	NA
1	460	1135	20197.5	0.17	8.33	2	0.17	8.33	0.83	2019	7.5	36	NA
1.83	461	1136	20197.5	0.17	9.16	2	0.17	9.16	1.66	2019	7.5	0	NA
2	462	1137	20197.5	0.17	9.33	2	0.17	9.33	1.83	2019	7.5	20	NA
3	463	1138	20197.5	0.17	10.33	2	0.17	10.33	2.83	2019	7.5	24	NA
3.67	464	1139	20197.5	0.17	11	2	0.17	11.00	3.50	2019	7.5	0	NA
3.84	465	1140	20197.5	0.17	11.17	2	0.17	11.17	3.67	2019	7.5	74	NA
4.17	466	1141	20197.5	0.17	11.5	2	0.17	11.50	4.00	2019	7.5	24	NA
4.75	467	1142	20197.5	0.17	12.08	2	0.17	12.08	4.58	2019	7.5	16	NA
1.83	468	1143	20197.5	1	8.33	3	1.00	8.33	1.66	2019	7.5	0	NA
2	469	1144	20197.5	1	8.5	3	1.00	8.50	1.83	2019	7.5	20	NA
3	470	1145	20197.5	1	9.5	3	1.00	9.50	2.83	2019	7.5	24	NA
3.67	471	1146	20197.5	1	10.17	3	1.00	10.17	3.50	2019	7.5	0	NA
3.84	472	1147	20197.5	1	10.34	3	1.00	10.34	3.67	2019	7.5	74	NA
4.17	473	1148	20197.5	1	10.67	3	1.00	10.67	4.00	2019	7.5	24	NA
4.75	474	1149	20197.5	1	11.25	3	1.00	11.25	4.58	2019	7.5	16	NA
2	475	1150	20197.5	1.83	7.67	4	1.83	7.67	1.83	2019	7.5	20	NA
3	476	1151	20197.5	1.83	8.67	4	1.83	8.67	2.83	2019	7.5	24	NA
3.67	477	1152	20197.5	1.83	9.34	4	1.83	9.34	3.50	2019	7.5	0	NA
3.84	478	1153	20197.5	1.83	9.51	4	1.83	9.51	3.67	2019	7.5	74	NA
4.17	479	1154	20197.5	1.83	9.84	4	1.83	9.84	4.00	2019	7.5	24	NA
4.75	480	1155	20197.5	1.83	10.42	4	1.83	10.42	4.58	2019	7.5	16	NA
3	481	1156	20197.5	2	8.5	5	2.00	8.50	2.83	2019	7.5	24	NA
3.67	482	1157	20197.5	2	9.17	5	2.00	9.17	3.50	2019	7.5	0	NA
3.84	483	1158	20197.5	2	9.34	5	2.00	9.34	3.67	2019	7.5	74	NA
4.17	484	1159	20197.5	2	9.67	5	2.00	9.67	4.00	2019	7.5	24	NA
4.75	485	1160	20197.5	2	10.25	5	2.00	10.25	4.58	2019	7.5	16	NA
3.67	486	1161	20197.5	3	8.17	6	3.00	8.17	3.50	2019	7.5	0	NA
3.84	487	1162	20197.5	3	8.34	6	3.00	8.34	3.67	2019	7.5	74	NA
4.17	488	1163	20197.5	3	8.67	6	3.00	8.67	4.00	2019	7.5	24	NA
4.75	489	1164	20197.5	3	9.25	6	3.00	9.25	4.58	2019	7.5	16	NA
3.84	490	1165	20197.5	3.67	7.67	7	3.67	7.67	3.67	2019	7.5	74	NA
4.17	491	1166	20197.5	3.67	8	7	3.67	8.00	4.00	2019	7.5	24	NA
4.75	492	1167	20197.5	3.67	8.58	7	3.67	8.58	4.58	2019	7.5	16	NA
4.17	493	1168	20197.5	3.84	7.83	8	3.84	7.83	4.00	2019	7.5	24	NA
4.75	494	1169	20197.5	3.84	8.41	8	3.84	8.41	4.58	2019	7.5	16	NA
4.75	495	1170	20197.5	4.17	8.08	9	4.17	8.08	4.58	2019	7.5	16	NA
0.17	496	1171	20158.5	0	8.67	1	0.00	8.67	0.00	2015	8.5	24	NA
1	497	1172	20158.5	0	9.5	1	0.00	9.50	0.83	2015	8.5	36	NA
1.83	498	1173	20158.5	0	10.33	1	0.00	10.33	1.66	2015	8.5	0	0
2	499	1174	20158.5	0	10.5	1	0.00	10.50	1.83	2015	8.5	20	NA
3	500	1175	20158.5	0	11.5	1	0.00	11.50	2.83	2015	8.5	24	NA
3.67	501	1176	20158.5	0	12.17	1	0.00	12.17	3.50	2015	8.5	0	0
3.84	502	1177	20158.5	0	12.34	1	0.00	12.34	3.67	2015	8.5	74	NA
4.17	503	1178	20158.5	0	12.67	1	0.00	12.67	4.00	2015	8.5	24	NA
4.75	504	1179	20158.5	0	13.25	1	0.00	13.25	4.58	2015	8.5	16	NA
1	505	1180	20158.5	0.17	9.33	2	0.17	9.33	0.83	2015	8.5	36	NA
1.83	506	1181	20158.5	0.17	10.16	2	0.17	10.16	1.66	2015	8.5	0	0
2	507	1182	20158.5	0.17	10.33	2	0.17	10.33	1.83	2015	8.5	20	NA
3	508	1183	20158.5	0.17	11.33	2	0.17	11.33	2.83	2015	8.5	24	NA
3.67	509	1184	20158.5	0.17	12	2	0.17	12.00	3.50	2015	8.5	0	0
3.84	510	1185	20158.5	0.17	12.17	2	0.17	12.17	3.67	2015	8.5	74	NA
4.17	511	1186	20158.5	0.17	12.5	2	0.17	12.50	4.00	2015	8.5	24	NA
4.75	512	1187	20158.5	0.17	13.08	2	0.17	13.08	4.58	2015	8.5	16	NA
1.83	513	1188	20158.5	1	9.33	3	1.00	9.33	1.66	2015	8.5	0	0
2	514	1189	20158.5	1	9.5	3	1.00	9.50	1.83	2015	8.5	20	NA
3	515	1190	20158.5	1	10.5	3	1.00	10.50	2.83	2015	8.5	24	NA
3.67	516	1191	20158.5	1	11.17	3	1.00	11.17	3.50	2015	8.5	0	0
3.84	517	1192	20158.5	1	11.34	3	1.00	11.34	3.67	2015	8.5	74	NA
4.17	518	1193	20158.5	1	11.67	3	1.00	11.67	4.00	2015	8.5	24	NA
4.75	519	1194	20158.5	1	12.25	3	1.00	12.25	4.58	2015	8.5	16	NA
2	520	1195	20158.5	1.83	8.67	4	1.83	8.67	1.83	2015	8.5	20	NA
3	521	1196	20158.5	1.83	9.67	4	1.83	9.67	2.83	2015	8.5	24	NA
3.67	522	1197	20158.5	1.83	10.34	4	1.83	10.34	3.50	2015	8.5	0	0
3.84	523	1198	20158.5	1.83	10.51	4	1.83	10.51	3.67	2015	8.5	74	NA
4.17	524	1199	20158.5	1.83	10.84	4	1.83	10.84	4.00	2015	8.5	24	NA
4.75	525	1200	20158.5	1.83	11.42	4	1.83	11.42	4.58	2015	8.5	16	NA
3	526	1201	20158.5	2	9.5	5	2.00	9.50	2.83	2015	8.5	24	NA
3.67	527	1202	20158.5	2	10.17	5	2.00	10.17	3.50	2015	8.5	0	0
3.84	528	1203	20158.5	2	10.34	5	2.00	10.34	3.67	2015	8.5	74	NA
4.17	529	1204	20158.5	2	10.67	5	2.00	10.67	4.00	2015	8.5	24	NA
4.75	530	1205	20158.5	2	11.25	5	2.00	11.25	4.58	2015	8.5	16	NA
3.67	531	1206	20158.5	3	9.17	6	3.00	9.17	3.50	2015	8.5	0	0
3.84	532	1207	20158.5	3	9.34	6	3.00	9.34	3.67	2015	8.5	74	NA
4.17	533	1208	20158.5	3	9.67	6	3.00	9.67	4.00	2015	8.5	24	NA
4.75	534	1209	20158.5	3	10.25	6	3.00	10.25	4.58	2015	8.5	16	NA
3.84	535	1210	20158.5	3.67	8.67	7	3.67	8.67	3.67	2015	8.5	74	NA
4.17	536	1211	20158.5	3.67	9	7	3.67	9.00	4.00	2015	8.5	24	NA
4.75	537	1212	20158.5	3.67	9.58	7	3.67	9.58	4.58	2015	8.5	16	NA
4.17	538	1213	20158.5	3.84	8.83	8	3.84	8.83	4.00	2015	8.5	24	NA
4.75	539	1214	20158.5	3.84	9.41	8	3.84	9.41	4.58	2015	8.5	16	NA
4.75	540	1215	20158.5	4.17	9.08	9	4.17	9.08	4.58	2015	8.5	16	NA
0.17	541	1216	20198.5	0	8.67	1	0.00	8.67	0.00	2019	8.5	24	NA
1	542	1217	20198.5	0	9.5	1	0.00	9.50	0.83	2019	8.5	36	NA
1.83	543	1218	20198.5	0	10.33	1	0.00	10.33	1.66	2019	8.5	0	NA
2	544	1219	20198.5	0	10.5	1	0.00	10.50	1.83	2019	8.5	20	NA
3	545	1220	20198.5	0	11.5	1	0.00	11.50	2.83	2019	8.5	24	NA
3.67	546	1221	20198.5	0	12.17	1	0.00	12.17	3.50	2019	8.5	0	NA
3.84	547	1222	20198.5	0	12.34	1	0.00	12.34	3.67	2019	8.5	74	NA
4.17	548	1223	20198.5	0	12.67	1	0.00	12.67	4.00	2019	8.5	24	NA
4.75	549	1224	20198.5	0	13.25	1	0.00	13.25	4.58	2019	8.5	16	NA
1	550	1225	20198.5	0.17	9.33	2	0.17	9.33	0.83	2019	8.5	36	NA
1.83	551	1226	20198.5	0.17	10.16	2	0.17	10.16	1.66	2019	8.5	0	NA
2	552	1227	20198.5	0.17	10.33	2	0.17	10.33	1.83	2019	8.5	20	NA
3	553	1228	20198.5	0.17	11.33	2	0.17	11.33	2.83	2019	8.5	24	NA
3.67	554	1229	20198.5	0.17	12	2	0.17	12.00	3.50	2019	8.5	0	NA
3.84	555	1230	20198.5	0.17	12.17	2	0.17	12.17	3.67	2019	8.5	74	NA
4.17	556	1231	20198.5	0.17	12.5	2	0.17	12.50	4.00	2019	8.5	24	NA
4.75	557	1232	20198.5	0.17	13.08	2	0.17	13.08	4.58	2019	8.5	16	NA
1.83	558	1233	20198.5	1	9.33	3	1.00	9.33	1.66	2019	8.5	0	NA
2	559	1234	20198.5	1	9.5	3	1.00	9.50	1.83	2019	8.5	20	NA
3	560	1235	20198.5	1	10.5	3	1.00	10.50	2.83	2019	8.5	24	NA
3.67	561	1236	20198.5	1	11.17	3	1.00	11.17	3.50	2019	8.5	0	NA
3.84	562	1237	20198.5	1	11.34	3	1.00	11.34	3.67	2019	8.5	74	NA
4.17	563	1238	20198.5	1	11.67	3	1.00	11.67	4.00	2019	8.5	24	NA
4.75	564	1239	20198.5	1	12.25	3	1.00	12.25	4.58	2019	8.5	16	NA
2	565	1240	20198.5	1.83	8.67	4	1.83	8.67	1.83	2019	8.5	20	NA
3	566	1241	20198.5	1.83	9.67	4	1.83	9.67	2.83	2019	8.5	24	NA
3.67	567	1242	20198.5	1.83	10.34	4	1.83	10.34	3.50	2019	8.5	0	NA
3.84	568	1243	20198.5	1.83	10.51	4	1.83	10.51	3.67	2019	8.5	74	NA
4.17	569	1244	20198.5	1.83	10.84	4	1.83	10.84	4.00	2019	8.5	24	NA
4.75	570	1245	20198.5	1.83	11.42	4	1.83	11.42	4.58	2019	8.5	16	NA
3	571	1246	20198.5	2	9.5	5	2.00	9.50	2.83	2019	8.5	24	NA
3.67	572	1247	20198.5	2	10.17	5	2.00	10.17	3.50	2019	8.5	0	NA
3.84	573	1248	20198.5	2	10.34	5	2.00	10.34	3.67	2019	8.5	74	NA
4.17	574	1249	20198.5	2	10.67	5	2.00	10.67	4.00	2019	8.5	24	NA
4.75	575	1250	20198.5	2	11.25	5	2.00	11.25	4.58	2019	8.5	16	NA
3.67	576	1251	20198.5	3	9.17	6	3.00	9.17	3.50	2019	8.5	0	NA
3.84	577	1252	20198.5	3	9.34	6	3.00	9.34	3.67	2019	8.5	74	NA
4.17	578	1253	20198.5	3	9.67	6	3.00	9.67	4.00	2019	8.5	24	NA
4.75	579	1254	20198.5	3	10.25	6	3.00	10.25	4.58	2019	8.5	16	NA
3.84	580	1255	20198.5	3.67	8.67	7	3.67	8.67	3.67	2019	8.5	74	NA
4.17	581	1256	20198.5	3.67	9	7	3.67	9.00	4.00	2019	8.5	24	NA
4.75	582	1257	20198.5	3.67	9.58	7	3.67	9.58	4.58	2019	8.5	16	NA
4.17	583	1258	20198.5	3.84	8.83	8	3.84	8.83	4.00	2019	8.5	24	NA
4.75	584	1259	20198.5	3.84	9.41	8	3.84	9.41	4.58	2019	8.5	16	NA
4.75	585	1260	20198.5	4.17	9.08	9	4.17	9.08	4.58	2019	8.5	16	NA
0.17	586	1261	20159.5	0	9.67	1	0.00	9.67	0.00	2015	9.5	24	NA
1	587	1262	20159.5	0	10.5	1	0.00	10.50	0.83	2015	9.5	36	NA
1.83	588	1263	20159.5	0	11.33	1	0.00	11.33	1.66	2015	9.5	0	0
2	589	1264	20159.5	0	11.5	1	0.00	11.50	1.83	2015	9.5	20	NA
3	590	1265	20159.5	0	12.5	1	0.00	12.50	2.83	2015	9.5	24	NA
3.67	591	1266	20159.5	0	13.17	1	0.00	13.17	3.50	2015	9.5	0	0
3.84	592	1267	20159.5	0	13.34	1	0.00	13.34	3.67	2015	9.5	74	NA
4.17	593	1268	20159.5	0	13.67	1	0.00	13.67	4.00	2015	9.5	24	NA
4.75	594	1269	20159.5	0	14.25	1	0.00	14.25	4.58	2015	9.5	16	NA
1	595	1270	20159.5	0.17	10.33	2	0.17	10.33	0.83	2015	9.5	36	NA
1.83	596	1271	20159.5	0.17	11.16	2	0.17	11.16	1.66	2015	9.5	0	0
2	597	1272	20159.5	0.17	11.33	2	0.17	11.33	1.83	2015	9.5	20	NA
3	598	1273	20159.5	0.17	12.33	2	0.17	12.33	2.83	2015	9.5	24	NA
3.67	599	1274	20159.5	0.17	13	2	0.17	13.00	3.50	2015	9.5	0	0
3.84	600	1275	20159.5	0.17	13.17	2	0.17	13.17	3.67	2015	9.5	74	NA
4.17	601	1276	20159.5	0.17	13.5	2	0.17	13.50	4.00	2015	9.5	24	NA
4.75	602	1277	20159.5	0.17	14.08	2	0.17	14.08	4.58	2015	9.5	16	NA
1.83	603	1278	20159.5	1	10.33	3	1.00	10.33	1.66	2015	9.5	0	0
2	604	1279	20159.5	1	10.5	3	1.00	10.50	1.83	2015	9.5	20	NA
3	605	1280	20159.5	1	11.5	3	1.00	11.50	2.83	2015	9.5	24	NA
3.67	606	1281	20159.5	1	12.17	3	1.00	12.17	3.50	2015	9.5	0	0
3.84	607	1282	20159.5	1	12.34	3	1.00	12.34	3.67	2015	9.5	74	NA
4.17	608	1283	20159.5	1	12.67	3	1.00	12.67	4.00	2015	9.5	24	NA
4.75	609	1284	20159.5	1	13.25	3	1.00	13.25	4.58	2015	9.5	16	NA
2	610	1285	20159.5	1.83	9.67	4	1.83	9.67	1.83	2015	9.5	20	NA
3	611	1286	20159.5	1.83	10.67	4	1.83	10.67	2.83	2015	9.5	24	NA
3.67	612	1287	20159.5	1.83	11.34	4	1.83	11.34	3.50	2015	9.5	0	0
3.84	613	1288	20159.5	1.83	11.51	4	1.83	11.51	3.67	2015	9.5	74	NA
4.17	614	1289	20159.5	1.83	11.84	4	1.83	11.84	4.00	2015	9.5	24	NA
4.75	615	1290	20159.5	1.83	12.42	4	1.83	12.42	4.58	2015	9.5	16	NA
3	616	1291	20159.5	2	10.5	5	2.00	10.50	2.83	2015	9.5	24	NA
3.67	617	1292	20159.5	2	11.17	5	2.00	11.17	3.50	2015	9.5	0	0
3.84	618	1293	20159.5	2	11.34	5	2.00	11.34	3.67	2015	9.5	74	NA
4.17	619	1294	20159.5	2	11.67	5	2.00	11.67	4.00	2015	9.5	24	NA
4.75	620	1295	20159.5	2	12.25	5	2.00	12.25	4.58	2015	9.5	16	NA
3.67	621	1296	20159.5	3	10.17	6	3.00	10.17	3.50	2015	9.5	0	0
3.84	622	1297	20159.5	3	10.34	6	3.00	10.34	3.67	2015	9.5	74	NA
4.17	623	1298	20159.5	3	10.67	6	3.00	10.67	4.00	2015	9.5	24	NA
4.75	624	1299	20159.5	3	11.25	6	3.00	11.25	4.58	2015	9.5	16	NA
3.84	625	1300	20159.5	3.67	9.67	7	3.67	9.67	3.67	2015	9.5	74	NA
4.17	626	1301	20159.5	3.67	10	7	3.67	10.00	4.00	2015	9.5	24	NA
4.75	627	1302	20159.5	3.67	10.58	7	3.67	10.58	4.58	2015	9.5	16	NA
4.17	628	1303	20159.5	3.84	9.83	8	3.84	9.83	4.00	2015	9.5	24	NA
4.75	629	1304	20159.5	3.84	10.41	8	3.84	10.41	4.58	2015	9.5	16	NA
4.75	630	1305	20159.5	4.17	10.08	9	4.17	10.08	4.58	2015	9.5	16	NA
0.17	631	1306	201510.5	0	10.67	1	0.00	10.67	0.00	2015	10.5	24	NA
1	632	1307	201510.5	0	11.5	1	0.00	11.50	0.83	2015	10.5	36	NA
1.83	633	1308	201510.5	0	12.33	1	0.00	12.33	1.66	2015	10.5	0	0
2	634	1309	201510.5	0	12.5	1	0.00	12.50	1.83	2015	10.5	20	NA
3	635	1310	201510.5	0	13.5	1	0.00	13.50	2.83	2015	10.5	24	NA
3.67	636	1311	201510.5	0	14.17	1	0.00	14.17	3.50	2015	10.5	0	0
3.84	637	1312	201510.5	0	14.34	1	0.00	14.34	3.67	2015	10.5	74	NA
4.17	638	1313	201510.5	0	14.67	1	0.00	14.67	4.00	2015	10.5	24	NA
4.75	639	1314	201510.5	0	15.25	1	0.00	15.25	4.58	2015	10.5	16	NA
1	640	1315	201510.5	0.17	11.33	2	0.17	11.33	0.83	2015	10.5	36	NA
1.83	641	1316	201510.5	0.17	12.16	2	0.17	12.16	1.66	2015	10.5	0	0
2	642	1317	201510.5	0.17	12.33	2	0.17	12.33	1.83	2015	10.5	20	NA
3	643	1318	201510.5	0.17	13.33	2	0.17	13.33	2.83	2015	10.5	24	NA
3.67	644	1319	201510.5	0.17	14	2	0.17	14.00	3.50	2015	10.5	0	0
3.84	645	1320	201510.5	0.17	14.17	2	0.17	14.17	3.67	2015	10.5	74	NA
4.17	646	1321	201510.5	0.17	14.5	2	0.17	14.50	4.00	2015	10.5	24	NA
4.75	647	1322	201510.5	0.17	15.08	2	0.17	15.08	4.58	2015	10.5	16	NA
1.83	648	1323	201510.5	1	11.33	3	1.00	11.33	1.66	2015	10.5	0	0
2	649	1324	201510.5	1	11.5	3	1.00	11.50	1.83	2015	10.5	20	NA
3	650	1325	201510.5	1	12.5	3	1.00	12.50	2.83	2015	10.5	24	NA
3.67	651	1326	201510.5	1	13.17	3	1.00	13.17	3.50	2015	10.5	0	0
3.84	652	1327	201510.5	1	13.34	3	1.00	13.34	3.67	2015	10.5	74	NA
4.17	653	1328	201510.5	1	13.67	3	1.00	13.67	4.00	2015	10.5	24	NA
4.75	654	1329	201510.5	1	14.25	3	1.00	14.25	4.58	2015	10.5	16	NA
2	655	1330	201510.5	1.83	10.67	4	1.83	10.67	1.83	2015	10.5	20	NA
3	656	1331	201510.5	1.83	11.67	4	1.83	11.67	2.83	2015	10.5	24	NA
3.67	657	1332	201510.5	1.83	12.34	4	1.83	12.34	3.50	2015	10.5	0	0
3.84	658	1333	201510.5	1.83	12.51	4	1.83	12.51	3.67	2015	10.5	74	NA
4.17	659	1334	201510.5	1.83	12.84	4	1.83	12.84	4.00	2015	10.5	24	NA
4.75	660	1335	201510.5	1.83	13.42	4	1.83	13.42	4.58	2015	10.5	16	NA
3	661	1336	201510.5	2	11.5	5	2.00	11.50	2.83	2015	10.5	24	NA
3.67	662	1337	201510.5	2	12.17	5	2.00	12.17	3.50	2015	10.5	0	0
3.84	663	1338	201510.5	2	12.34	5	2.00	12.34	3.67	2015	10.5	74	NA
4.17	664	1339	201510.5	2	12.67	5	2.00	12.67	4.00	2015	10.5	24	NA
4.75	665	1340	201510.5	2	13.25	5	2.00	13.25	4.58	2015	10.5	16	NA
3.67	666	1341	201510.5	3	11.17	6	3.00	11.17	3.50	2015	10.5	0	0
3.84	667	1342	201510.5	3	11.34	6	3.00	11.34	3.67	2015	10.5	74	NA
4.17	668	1343	201510.5	3	11.67	6	3.00	11.67	4.00	2015	10.5	24	NA
4.75	669	1344	201510.5	3	12.25	6	3.00	12.25	4.58	2015	10.5	16	NA
3.84	670	1345	201510.5	3.67	10.67	7	3.67	10.67	3.67	2015	10.5	74	NA
4.17	671	1346	201510.5	3.67	11	7	3.67	11.00	4.00	2015	10.5	24	NA
4.75	672	1347	201510.5	3.67	11.58	7	3.67	11.58	4.58	2015	10.5	16	NA
4.17	673	1348	201510.5	3.84	10.83	8	3.84	10.83	4.00	2015	10.5	24	NA
4.75	674	1349	201510.5	3.84	11.41	8	3.84	11.41	4.58	2015	10.5	16	NA
4.75	675	1350	201510.5	4.17	11.08	9	4.17	11.08	4.58	2015	10.5	16	NA

Now let’s build models. We’ll consider four possible survival models in which survival varies temporaly, by release size, or release cohort. We’ll also consider whether detection varies by year or effort.

We’ll run all combinations of these models as well as nulls—Phi(.) and p(.)—for a total of 16 CJS models.

# apparent survival (Phi)
Phi.dot = list(formula=~1)
Phi.time = list(formula=~time)
Phi.length = list(formula=~length)
Phi.cohort = list(formula=~release_cohort)

# detection (p)
p.dot = list(formula=~1)
p.time = list(formula=~time)
p.effort = list(formula=~effort)
p.length = list(formula=~length)

Let’s first examine goodness of fit for our data before ranking models.

RGOF <- release.gof(tortoises.process)
RGOF

##       Chi.square df      P
## TEST2    45.5195 38 0.1876
## TEST3     0.0000  0 1.0000
## Total    45.5195 38 0.1876

chat <- RGOF$Chi.square[3]/RGOF$df[3]
chat

## [1] 1.197882

There is no lack of model fit. We’ll still account for slight overdispersion with c-hat.

Model outcomes

# make and model list
tortoises.list <- create.model.list("CJS")

tortoises.results <- mark.wrapper(tortoises.list,
                                  data=tortoises.process,
                                  ddl=tortoises.ddl,
                                  output = FALSE)

tortoises.results <- adjust.chat(chat, tortoises.results)

aic.table.tortoises <- model.table(tortoises.results, 
                                   use.lnl = TRUE, use.AIC = TRUE)
aic.table.tortoises$model <- gsub("~", "", aic.table.tortoises$model)
aic.table.tortoises$model <- gsub("1", ".", aic.table.tortoises$model)
aic.table.tortoises$model <- gsub(")", ") ", aic.table.tortoises$model)

kable(aic.table.tortoises[,3:8], "html", 
      caption = "AIC tortoise model rankings", digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "condensed")) %>%
  scroll_box(height = "300px")

AIC tortoise model rankings

	model	npar	QAIC	DeltaQAIC	weight	Neg2LnL
8	Phi(.) p(time)	10	2989.460	0.000	0.559	3557.062
12	Phi(length) p(time)	11	2990.930	1.470	0.268	3556.426
4	Phi(release_cohort) p(time)	12	2992.086	2.626	0.150	3555.416
16	Phi(time) p(time)	18	2995.925	6.465	0.022	3545.640
14	Phi(time) p(effort)	11	3010.554	21.094	0.000	3579.934
13	Phi(time) p(.)	10	3014.530	25.070	0.000	3587.093
15	Phi(time) p(length)	11	3015.730	26.270	0.000	3586.134
2	Phi(release_cohort) p(effort)	5	3072.485	83.025	0.000	3668.494
6	Phi(.) p(effort)	3	3075.496	86.036	0.000	3676.892
10	Phi(length) p(effort)	4	3077.215	87.754	0.000	3676.556
3	Phi(release_cohort) p(length)	5	3101.685	112.224	0.000	3703.472
1	Phi(release_cohort) p(.)	4	3101.869	112.408	0.000	3706.088
5	Phi(.) p(.)	2	3110.692	121.232	0.000	3721.449
7	Phi(.) p(length)	3	3111.162	121.702	0.000	3719.617
11	Phi(length) p(length)	4	3112.369	122.909	0.000	3718.666
9	Phi(length) p(.)	3	3112.439	122.978	0.000	3721.146

write.csv(aic.table.tortoises[,3:8], "data/santafe_CJS_aictab_2020.csv")

It doesn’t look like any variable strongly influences survival, as the top survival model is the null model Phi(.). There is some strong evidence for time-varying detection, but not much support for effort as a driver of detection variability.

Let’s look at what the top model says about apparent survival.

# beta estimates
kable(tortoises.results$Phi.dot.p.time$results$beta, "html", 
      caption = "Beta estimates of Phi(.)p(time)") %>% 
  kable_styling(bootstrap_options = c("striped", "condensed"))

Beta estimates of Phi(.)p(time)

	estimate	se	lcl	ucl
Phi:(Intercept)	2.8733159	0.1560346	2.5674880	3.1791438
p:(Intercept)	0.2111451	0.1420148	-0.0672039	0.4894942
p:time1	1.0561319	0.2260769	0.6130213	1.4992426
p:time1.83	-0.0999540	399.5444200	-783.2070300	783.0071200
p:time2	0.5895949	0.1815080	0.2338393	0.9453506
p:time3	1.0517683	0.1938112	0.6718983	1.4316383
p:time3.67	-0.0999886	399.5570000	-783.2317200	783.0317500
p:time3.84	0.8279971	0.1794259	0.4763224	1.1796718
p:time4.17	0.2919220	0.1737210	-0.0485712	0.6324152
p:time4.75	-0.5501735	0.1731062	-0.8894616	-0.2108853

# real estimates
kable(tortoises.results$Phi.dot.p.time$results$real, "html", 
      caption = "Real estimates of Phi(.)p(time)") %>% 
  kable_styling(bootstrap_options = c("striped", "condensed"))

Real estimates of Phi(.)p(time)

	estimate	se	lcl	ucl	fixed	note
Phi g20154.5 c0 a4.5 t0	0.9465115	0.0078996	0.9287396	0.9600418
p g20154.5 c0 a4.67 t0.17	0.5525910	0.0351109	0.4832053	0.6199873
p g20154.5 c0 a5.5 t1	0.7802763	0.0302776	0.7152737	0.8338853
p g20174.5 c0 a6.33 t1.83	0.5277692	99.5780110	0.0000000	1.0000000
p g20154.5 c0 a6.5 t2	0.6901328	0.0241988	0.6408257	0.7354652
p g20154.5 c0 a7.5 t3	0.7795272	0.0226773	0.7319020	0.8207641
p g20195.5 c0 a9.17 t3.67	0.5277606	99.5813480	0.0000000	1.0000000
p g20154.5 c0 a8.34 t3.84	0.7386845	0.0211789	0.6951047	0.7780244
p g20154.5 c0 a8.67 t4.17	0.6231799	0.0235085	0.5761165	0.6680288
p g20154.5 c0 a9.25 t4.75	0.4160455	0.0240607	0.3697856	0.4638333
p g20154.5 c0 a6.33 t1.83	0.0000000	0.0000000	0.0000000	0.0000000	Fixed

The model states there is an overall annual survival rate of 0.947.

Because there was model uncertainty, we should still model average to plot our survival estimates.

# survival
tortoises.mod.avg.phi <- model.average(tortoises.results,"Phi", vcv=TRUE, drop = FALSE)
tortoises.mod.avg.phi.unique <- unique(tortoises.mod.avg.phi$estimates[,2:5])

kable(tortoises.mod.avg.phi.unique, "html", 
      caption = "Model-averaged Phi estimates") %>% 
  kable_styling(bootstrap_options = c("striped", "condensed")) %>% 
  scroll_box(height = "300px")

Model-averaged Phi estimates

	estimate	se	lcl	ucl
Phi g20154.5 c0 a4.5 t0	0.9438413	0.0214413	0.8838025	0.9737787
Phi g20154.5 c0 a4.67 t0.17	0.9463811	0.0102846	0.9222636	0.9633139
Phi g20154.5 c0 a5.5 t1	0.9469669	0.0118273	0.9183969	0.9659055
Phi g20154.5 c0 a6.33 t1.83	0.9432798	0.0228634	0.8780059	0.9746373
Phi g20154.5 c0 a6.5 t2	0.9463782	0.0100616	0.9228759	0.9630056
Phi g20154.5 c0 a7.5 t3	0.9442878	0.0153745	0.9052906	0.9677987
Phi g20154.5 c0 a8.17 t3.67	0.9469670	0.0118271	0.9183976	0.9659054
Phi g20154.5 c0 a8.34 t3.84	0.9469641	0.0118397	0.9183580	0.9659190
Phi g20154.5 c0 a8.67 t4.17	0.9365481	4.0955741	0.0000000	1.0000000
Phi g20174.5 c0 a4.5 t0	0.9461196	0.0221034	0.8824435	0.9762336
Phi g20174.5 c0 a4.67 t0.17	0.9486594	0.0110919	0.9220268	0.9665256
Phi g20174.5 c0 a5.5 t1	0.9492451	0.0124288	0.9185677	0.9687587
Phi g20174.5 c0 a6.33 t1.83	0.9455581	0.0235399	0.8763583	0.9770427
Phi g20174.5 c0 a6.5 t2	0.9486565	0.0108862	0.9226174	0.9662540
Phi g20174.5 c0 a7.5 t3	0.9465660	0.0162226	0.9042839	0.9707739
Phi g20174.5 c0 a8.17 t3.67	0.9492452	0.0124286	0.9185684	0.9687586
Phi g20174.5 c0 a8.34 t3.84	0.9492424	0.0124412	0.9185277	0.9687714
Phi g20174.5 c0 a8.67 t4.17	0.9388264	4.0955817	0.0000000	1.0000000
Phi g20195.5 c0 a5.5 t0	0.9525144	0.0288849	0.8515767	0.9859410
Phi g20195.5 c0 a5.67 t0.17	0.9550542	0.0208884	0.8911515	0.9821907
Phi g20195.5 c0 a6.5 t1	0.9556399	0.0214541	0.8887595	0.9830759
Phi g20195.5 c0 a7.33 t1.83	0.9519529	0.0301179	0.8449774	0.9863049
Phi g20195.5 c0 a7.5 t2	0.9550513	0.0207808	0.8916263	0.9821023
Phi g20195.5 c0 a8.5 t3	0.9529608	0.0245610	0.8737694	0.9834141
Phi g20195.5 c0 a9.17 t3.67	0.9556400	0.0214539	0.8887603	0.9830759
Phi g20195.5 c0 a9.34 t3.84	0.9556371	0.0214621	0.8887223	0.9830800
Phi g20195.5 c0 a9.67 t4.17	0.9452212	4.0956353	0.0000000	1.0000000

# detection
# remove the fully time dependent model: Phi(time)p(time)
# so we can estimate the variance for detection in the last occasion
tortoises.results.omit <- remove.mark(tortoises.results, 16)
tortoises.mod.avg.p <- model.average(tortoises.results.omit, "p", 
                                     vcv=TRUE, drop = FALSE)
tortoises.mod.avg.p.unique <- unique(tortoises.mod.avg.p$estimates[,2:5])

kable(tortoises.mod.avg.p.unique, "html", 
      caption = "Model-averaged p estimates") %>% 
  kable_styling(bootstrap_options = c("striped", "condensed"))

Model-averaged p estimates

	estimate	se	lcl	ucl
p g20154.5 c0 a4.67 t0.17	0.5525945	0.0384326	0.4766376	0.6261736
p g20154.5 c0 a5.5 t1	0.7802715	0.0331396	0.7085604	0.8383628
p g20154.5 c0 a6.33 t1.83	0.0000000	0.0000000	0.0000000	0.0000000
p g20154.5 c0 a6.5 t2	0.6901172	0.0264839	0.6359769	0.7395034
p g20154.5 c0 a7.5 t3	0.7794498	0.0248293	0.7269848	0.8242698
p g20154.5 c0 a8.34 t3.84	0.7381662	0.0231903	0.6902510	0.7810208
p g20154.5 c0 a8.67 t4.17	0.6221957	0.0257553	0.5705596	0.6712011
p g20154.5 c0 a9.25 t4.75	0.4146342	0.0264133	0.3639793	0.4671607
p g20174.5 c0 a6.33 t1.83	0.5277348	100.1423196	0.0000000	1.0000000
p g20195.5 c0 a9.17 t3.67	0.5277205	100.1467970	0.0000000	1.0000000

Let’s use the overall survival estimates from the first model to get a quick estimate of abundance, using the following calculations.

phi <- tortoises.results$Phi.dot.p.time$results$real[1,1]
lwr <- tortoises.results$Phi.dot.p.time$results$real[1,3]
upr <- tortoises.results$Phi.dot.p.time$results$real[1,4]

N_2015 <- 205
N_2016 <- N_2015 * phi
N_2017 <- N_2016 * phi + 191*phi^(2/12)
N_2018 <- N_2017 * phi 
N_2019 <- N_2018 * phi + 155*phi^(4/12)
# add the final 34 individuals that were added in December of 2019
N_2020 <- N_2019 * phi^(8/12) + 34

# get the lower and upper confidence intervals
# lower 95% CL
N_2015_lwr <- 205
N_2016_lwr <- N_2015_lwr * lwr
N_2017_lwr <- N_2016_lwr * lwr + 191*lwr^(2/12)
N_2018_lwr <- N_2017_lwr * lwr 
N_2019_lwr <- N_2018_lwr * lwr + 155*lwr^(4/12)
# add the final 34 individuals that were added in December of 2019
N_2020_lwr <- N_2019_lwr * lwr^(8/12) + 34

# upper 95% CL
N_2015_upr <- 205
N_2016_upr <- N_2015_upr * upr
N_2017_upr <- N_2016_upr * upr + 191*upr^(2/12)
N_2018_upr <- N_2017_upr * upr
N_2019_upr <- N_2018_upr * upr + 155*upr^(4/12)
# add the final 34 individuals that were added in December of 2019
N_2020_upr <- N_2019_upr * upr^(8/12) + 34

santafe_pop_15_20 <- 
  data.frame(Year = c("2015", "2016", "2017", "2018", "2019", "2020"),
             N = c(N_2015,N_2016, N_2017, N_2018, N_2019, N_2020),
             lcl = c(N_2015_lwr,N_2016_lwr, N_2017_lwr, 
                     N_2018_lwr, N_2019_lwr, N_2020_lwr),
             ucl = c(N_2015_upr,N_2016_upr, N_2017_upr, 
                     N_2018_upr, N_2019_upr, N_2020_upr))

kable(santafe_pop_15_20, 
      caption = "Population estimates (2015-2020) of the 
      tortoises released on Santa Fe.") %>%
  kable_styling(bootstrap_options = c("striped", "condensed"))

Population estimates (2015-2020) of the tortoises released on Santa Fe.

Year	N	lcl	ucl
2015	205.0000	205.0000	205.0000
2016	194.0349	190.3916	196.8086
2017	372.9143	365.4853	378.6507
2018	352.9676	339.4407	363.5205
2019	486.2736	466.4791	501.9023
2020	502.7752	478.0463	522.4415

Let’s also track the estimated population size of each cohort individually.

Population estimates of tortoises on Santa Fe (2015-2020).

Year	N	lcl	ucl
First release cohort (2015)
Release (June 2015)	205.0000	205.0000	205.0000
2016	194.0349	190.3916	196.8086
2017	183.6562	176.8242	188.9445
2018	173.8327	164.2237	181.3946
2019	164.5347	152.5210	174.1464
2020 (March)	157.8890	146.3606	167.1125
Second release cohort (2017)
Release (Apr 2017)	191.0000	191.0000	191.0000
2018	180.7837	177.3893	183.3680
2019	171.1138	164.7484	176.0409
2020 (March)	162.7049	153.9539	169.5819
Third release cohort (2019)
Release (Feb 2019)	155.0000	155.0000	155.0000
2020 (March)	146.0387	143.0705	148.3017

Let’s put these estimates of survival, detection, and population size together in a single figure.

# create the df for plotting population parameter estimates
tortoises.mod.avg.phi.unique$cohort <- 
  c(rep("2015",9), rep("2017",9), rep("2019", 9))

tortoises.mod.avg.phi.unique$year <- 
  c(rep(c(2015,2015,2016,2017,2017,2018,2019,2019,2019),3))

tortoises.phi.df <- tortoises.mod.avg.phi.unique %>%
  filter(ucl != 1) %>%
  group_by(year) %>%
  summarise(phi = mean(estimate),
            se = mean(se),
            lcl = mean(lcl),
            ucl = mean(ucl)) %>%
  ungroup() %>%
  mutate(time = c(2015.5, 2016.5, 2017.5, 2018.5, 2019.5))

det.df <- tortoises.mod.avg.p.unique[c(1:2,4:8),] %>%
  mutate(year = decimal_date(as.Date(c("2015-08-01", "2016-06-01", 
                                       "2017-06-01", "2018-06-01",
                                       "2019-04-01", "2019-08-01", 
                                       "2020-03-01"), 
                                     format = "%Y-%m-%d")))

scaleFUN <- function(x) sprintf("%.2f", x)

espanola.phi <- data.frame(stage = c("juvenile", "subadult/adult"),
                           phi = c(0.931, 0.979),
                           lcl = c(0.902, 0.927),
                           ucl = c(0.951, 0.992))

santafe.phi.plot <- 
  ggplot(tortoises.phi.df,  aes(x = time, y = phi)) +
  geom_hline(data = espanola.phi, inherit.aes = FALSE, 
             aes(yintercept = phi), lty = "dashed", lwd = 1.1, col = "grey") +
  geom_pointrange(aes(ymin = lcl, ymax = ucl)) +
  geom_point(size = 2) +
  labs(y = expression(paste("Apparent survival ( ", phi, ")")), x = "Year") + 
  scale_y_continuous(limits = c(floor_any(min(tortoises.phi.df$lcl),0.05), 1), 
                     labels = scaleFUN) + 
  xlim(2015,2020.5) + 
  theme(legend.position = "top") + 
  annotate("text", x = 2020.15, y = 0.94, 
           label = "juvenile", size = 4, col = "grey25") +
  annotate("text", x = 2020.15, y = 0.99, 
           label = "(sub)adult", size = 4, col = "grey25") + 
  theme_classic() + mythemes
  
santafe.p.plot <- 
  ggplot(det.df, aes(x = year, y = estimate)) +  geom_line() + 
  geom_pointrange(aes(ymin = lcl, ymax = ucl)) +
  geom_hline(aes(yintercept = mean(det.df$estimate)), lty = "dashed") +
  geom_point(size = 2) +
  ylab("Detection probability") + xlab("Year") +
  scale_y_continuous(limits = c(0.3,1), labels = scaleFUN) +
  xlim(2015,2020.5) + theme_classic() + mythemes

santafe.n.plot <- 
  ggplot(data = total_pop) +
  geom_line(aes(x = Year, y = N_cum), color = "black") +
  geom_line(aes(x = Year, y = N_hat), color = "black") +
  geom_ribbon(aes(x = Year, ymin = lwr, ymax = upr), alpha = 0.5) +
  annotate("text", 
           x = decimal_date(as.Date("2015-06-01", format = "%Y-%m-%d")), 
           y = 205+34, label = "Release 1", size = 4) +
  annotate("text", 
           x = decimal_date(as.Date("2017-04-01", format = "%Y-%m-%d")),  
           y = 396+34, label = "Release 2", size = 4) +
  annotate("text", 
           x = decimal_date(as.Date("2019-02-01", format = "%Y-%m-%d")),
           y = 551+34, label = "Release 3", size = 4) +
  annotate("text", 
           x = decimal_date(as.Date("2020-05-05", format = "%Y-%m-%d")),
           y = 551, label = 551, size = 4) +
  annotate("text", 
           x = decimal_date(as.Date("2020-05-05", format = "%Y-%m-%d")),
           y = last(total_pop$N_hat), 
           label = round(last(total_pop$N_hat),0), size = 4) +
  annotate("text", 
           x = decimal_date(as.Date("2020-05-05", format = "%Y-%m-%d")),
           y = last(total_pop$N_hat) * 0.88, 
           label = paste("(",round(last(total_pop$N_hat)/551*100,1),"%",")", 
                         sep = ""), size = 4) +
  ylab("Population size") + xlab("Year") +
  xlim(2015,2020.5) + ylim(0,600) + theme_classic() + mythemes

# combine survival, detection, and N figures
library(cowplot)
ggdraw() +
  draw_plot(santafe.phi.plot, x = 0, y = .4, width = .5, height = .6) +
  draw_plot(santafe.p.plot, x = .5, y = .4, width = .5, height = .6) +
  draw_plot(santafe.n.plot, x = 0, y = 0, width = 1, height = 0.4) +
  draw_plot_label(label = c("A", "B", "C"), size = 15,
                  x = c(0.1, 0.6, 0.1), y = c(1, 1, 0.4))

Population projections

---

We’ll make deterministic and stochastic population projections in the R package popbio. These will be female-only models, making the assumption that approximately half of all tortoise eggs become female.

Let’s first create our Leslie matrices.

library(popbio)

# hatching viability parameter estimates and quantiles from kevin'a ABC
egghatchvia <- c(0.3447368, 0.2305263, 0.2636842, 0.3005263, 0.3078947, 
                 0.3447368, 0.3815789, 0.4184211, 0.418421, 0.4184211)

names(egghatchvia) <- c("mean", "p025", "p05", "p10", "p25", 
                        "p50", "p75", "p90", "p95", "p975")

# starting female population in 2020
n_2020 <- c(0, 0, round(last(total_pop$N_hat)/2), 20)

# vital rates
propfem <- 0.5 # proportion of population that is female
repro <- 17 # reproductive age
# mean annual number of female eggs produced
F1 <- 3
F1_lwr <- 2 
F1_upr <- 4 
# survivorship from egg to juvenile (age 1) (from Kevin's Espnola ABC)
G1 <- egghatchvia["mean"] 
G1_lwr <- egghatchvia["p025"]
G1_upr <- egghatchvia["p975"]
# annual survival, phi (1-4 yrs)
p1 <- 0.75 
p1_lwr <- 0.6
p1_upr <- 0.9
# young juvenile stage survival parameter for matrix
P1 <- (1-p1^(3-1))*p1/(1-p1^3)
P1_lwr <- (1-p1_lwr^(3-1))*p1_lwr/(1-p1_lwr^3)
P1_upr <- (1-p1_upr^(3-1))*p1_upr/(1-p1_upr^3)
# juvenile/subadult survival (4-17 yrs) (Santa Fe rates)
p2 <- tortoises.results$Phi.dot.p.time$results$real$estimate[1]
p2_lwr <- tortoises.results$Phi.dot.p.time$results$real$lcl[1]
p2_upr <- tortoises.results$Phi.dot.p.time$results$real$ucl[1]
# juvenile/subadult stage survival parameter for matrix
P2 <- (1-p2^(13-1))*p2/(1-p2^13)
P2_lwr <- (1-p2_lwr^(13-1))*p2_lwr/(1-p2_lwr^13)
P2_upr <- (1-p2_upr^(13-1))*p2_upr/(1-p2_upr^13)
# survivorship from 1 to 4 (using the range from Gibbs et al. 2014)
G2 <- round(p1^3*(1-p1)/(1-p1^3),3) 
G2_lwr <- round(p1_lwr^3*(1-p1_lwr)/(1-p1_lwr^3),3)
G2_upr <- round(p1_upr^3*(1-p1_upr)/(1-p1_upr^3),3)
# survivorship from 4 to 17 (using the subadult/adult survival rates from Espanola)
G3 <- round(p2^13*(1-p2)/(1-p2^13),3) 
G3_lwr <- round(p2_lwr^13*(1-p2_lwr)/(1-p2_lwr^13),3)
G3_upr <- round(p2_upr^13*(1-p2_upr)/(1-p2_upr^13),3)
# annual survival for adult stage, phi (8 + years old)
P3 <- 0.979 
P3_lwr <- 0.927
P3_upr <- 0.992

# make matrices
stages <- c("egg/hatchling", "young juvenile", "juvenile/subadult", "adult")
tortoise.matrix <- matrix(c(0, 0, 0, F1,
                            G1, P1, 0, 0,
                            0, G2, P2, 0,
                            0, 0, G3, P3),
                          nrow = 4, ncol = 4, byrow = T)
tortoise.matrix.lwr <- matrix(c(0, 0, 0, F1_lwr,
                                G1_lwr, P1_lwr, 0, 0,
                                0, G2_lwr, P2_lwr, 0,
                                0, 0, G3_lwr, P3_lwr),
                              nrow = 4, ncol = 4, byrow = T)
tortoise.matrix.upr <- matrix(c(0, 0, 0, F1_upr,
                                G1_upr, P1_upr, 0, 0,
                                0, G2_upr, P2_upr, 0,
                                0, 0, G3_upr, P3_upr),
                              nrow = 4, ncol = 4, byrow = T)

Now let’s run the deterministic projection to extract stable stage proportions and population growth rates.

We will project the Santa Fe population from 2020 to 2100.

set.seed(123)

it <- 81 # time steps for model

# deterministic model
tortoise.proj <- pop.projection(tortoise.matrix, n_2020, it)
tortoise.proj.lwr <- pop.projection(tortoise.matrix.lwr, n_2020, it)
tortoise.proj.upr <- pop.projection(tortoise.matrix.upr, n_2020, it)

proj.df <- data.frame(Year = c(2020:2100), 
                      N_projected = tortoise.proj$stage.vectors[4,],
                      N_proj_lwr = tortoise.proj.lwr$stage.vectors[4,],
                      N_proj_upr = tortoise.proj.upr$stage.vectors[4,])

# time to saturation (K = 1500 female tortoises)
min(proj.df$Year[proj.df$N_projected >= 1500]) # max year at saturation

## [1] 2068

min(proj.df$Year[proj.df$N_proj_upr >= 1500]) # earliest year at saturation

## [1] 2046

# plot projection (without density dependence)
ggplot(proj.df, aes(Year, N_projected)) + geom_line(col = "blue", lwd = 1.1) + 
  geom_line(aes(x = Year, y = N_proj_lwr), col = "grey10") +
  geom_line(aes(x = Year, y = N_proj_upr), col = "grey10") +
  theme_classic() + xlim(2020, 2050) + ylim(0,1500)

# minimum adult population size
min(proj.df[,2:4]) 

## [1] 12.41394

# population growth rate
tortoise.proj$lambda 

## [1] 1.076044

tortoise.proj.lwr$lambda

## [1] 0.9774327

tortoise.proj.upr$lambda

## [1] 1.157446

# stable stages 
tortoise.proj$stable.stage 

## [1] 0.3677598 0.2493339 0.2509978 0.1319085

tortoise.proj.lwr$stable.stage 

## [1] 0.3965698 0.1874751 0.2221450 0.1938102

tortoise.proj.upr$stable.stage 

## [1] 0.34199152 0.27181411 0.28723519 0.09895918

# generation time
generation.time(tortoise.matrix)

## [1] 31.5414

generation.time(tortoise.matrix.lwr)

## [1] 28.71707

generation.time(tortoise.matrix.upr)

## [1] 30.73834

Without any other constraints on the tortoise population, these vital rates should ensure long-term persistence without future releases. Growth rates are very high, and the stable stage proportion for adult is between 0.1–0.2.

Now let’s create our stochastic model.

# stochastic projection (with density dependence)
tortoise.matrices <- list(tortoise.matrix, tortoise.matrix.lwr, 
                          tortoise.matrix.upr)
# nmax = K = K for Santa Fe (3000) divided by 2 times the stable stage prop. for adults
tortoise.proj.stoch <- 
  stoch.projection(matrices = tortoise.matrices,
                   n0 = n_2020, 
                   tmax = it, 
                   nreps = 10000,
                   prob = c(0.68, 0.16, 0.16),
                   nmax = 1500/tortoise.proj$stable.stage[4])

final.fem.pop <- tortoise.proj.stoch[,4]
hist(final.fem.pop, main = "Santa Fe adult female pop. in 2100", 
     xlab = "N adults")
abline(v = mean(final.fem.pop), col = "red", lwd = 2)

Almost all of our stochastic projections end with a female adult population > 1000 individuals. The mean projection for 2100 is just below 1500.

Let’s run the stochastic projection again, but this time we’ll put the projections in a for loop that will let us get population size estimates at each time step so we can plot out the projected female population from 2020 to 2100.

extin=c()
popQuant = matrix(NA, 3, 82)
popQuant[,1] = rep(sum(n_2020), 3)
popMean = vector('numeric', 82)
popMean[1] = sum(n_2020)
popSD   = vector('numeric', 82)
popSD[1] = NA

for(i in 1:81){
  matriz=c()
  interactionX=10000
  quasi=75
  popExtinctProject <- 
    stoch.projection(matrices=tortoise.matrices, n0=n_2020, tmax=i, 
                     nmax = 1500/tortoise.proj$stable.stage[4], 
                     nreps = interactionX, 
                     prob = c(0.68, 0.16, 0.16), verbose=FALSE)
  for(ii in 1:interactionX){
    a <- popExtinctProject[ii,4]
    matriz <- rbind(matriz,c(a))
  }
  vv <- matriz[matriz<quasi]
  s <- length(vv)
  extin <- c(extin,s)
  
  popQuant[,i+1] <- quantile(popExtinctProject[,4], probs=c(0.025, 0.5, 0.975))
  popMean[i+1] <- mean(popExtinctProject[,4])
  popSD[i+1] <- sd(popExtinctProject[,4])
}

stoch.proj.df <- data.frame(Year = c(2020:2100), 
                            N_projected = c(n_2020[4],popMean[2:81]),
                            N_proj_med = c(n_2020[4],popQuant[2,2:81]),
                            N_proj_lwr = c(n_2020[4],popQuant[1,2:81]),
                            N_proj_upr = c(n_2020[4],popQuant[3,2:81]))

# table of stochastic projections (annual means across iterations)
kable(stoch.proj.df) %>%
  kable_styling(bootstrap_options = c("striped", "condensed")) %>% 
  scroll_box(height = "300px")

Year	N_projected	N_proj_med	N_proj_lwr	N_proj_upr
2020	20.00000	20.00000	20.00000	20.00000
2021	31.35200	31.51400	28.83600	33.17800
2022	41.14566	41.53612	35.83882	44.95530
2023	49.58904	50.22864	44.10959	53.69153
2024	56.94024	57.92870	51.04890	61.63168
2025	63.53890	63.72569	56.22097	69.04136
2026	69.75895	69.48694	60.44117	77.91868
2027	75.85269	75.76439	65.19647	85.70249
2028	81.93094	81.97097	69.87710	93.75009
2029	88.09195	88.21603	73.76498	102.23745
2030	94.48232	94.47263	77.45783	112.00050
2031	101.54580	101.48743	82.16992	122.09223
2032	108.74008	108.49236	86.30035	132.83760
2033	116.58290	115.95879	90.95143	145.28897
2034	124.80682	123.92487	96.08951	158.17859
2035	133.61245	132.72855	100.78975	171.12170
2036	143.44269	142.45064	106.25213	186.51732
2037	153.43908	151.95236	111.71132	201.83413
2038	164.54999	162.81035	118.26941	219.74081
2039	176.68384	174.73113	125.30766	239.69477
2040	189.55221	187.59238	131.57494	259.70921
2041	202.58162	199.39012	140.27402	282.74356
2042	216.90881	213.99125	146.37978	305.07998
2043	232.09107	228.00715	154.90188	331.35909
2044	248.75898	244.95739	163.32701	354.45655
2045	266.60918	261.72329	174.03482	389.86121
2046	285.87687	280.25645	182.30603	419.64687
2047	306.55423	299.98379	195.02205	453.15409
2048	329.26078	321.31593	206.36077	493.91536
2049	351.68720	344.61918	217.80670	524.63756
2050	378.90360	370.59224	232.43769	577.39504
2051	403.85692	393.23159	242.99478	620.63475
2052	433.16520	421.52331	256.97200	672.62053
2053	462.88972	452.01523	271.85951	725.47862
2054	500.13432	488.12765	293.87717	784.79338
2055	536.14800	522.81365	312.66506	849.19281
2056	570.99695	553.87310	328.82871	918.71309
2057	613.06685	595.43593	347.83700	987.64256
2058	656.84293	636.20461	364.30218	1077.68949
2059	704.71241	683.10129	390.03297	1146.23159
2060	755.50700	729.84283	419.73771	1237.84476
2061	806.71774	784.57866	437.76005	1307.24346
2062	860.35991	832.05764	469.46271	1387.83461
2063	918.57302	889.76281	501.21510	1438.42960
2064	981.60545	960.42454	534.29004	1488.36448
2065	1033.49947	1027.76733	565.31707	1499.60668
2066	1092.48728	1095.82393	588.29632	1522.64144
2067	1147.69066	1172.02788	637.81851	1547.95792
2068	1196.00715	1238.81549	666.71948	1557.72264
2069	1246.24031	1291.49855	712.68675	1573.34961
2070	1292.28332	1336.38883	764.34160	1595.39479
2071	1324.08663	1374.58449	808.57528	1602.15423
2072	1355.71792	1404.65550	857.24457	1610.25845
2073	1380.37400	1427.33179	914.27047	1617.70955
2074	1400.75478	1439.09491	980.36527	1621.61076
2075	1416.24521	1453.13790	1027.92711	1620.22698
2076	1429.06069	1461.04824	1093.64717	1627.67874
2077	1439.00925	1470.04710	1157.14405	1628.85139
2078	1446.38514	1475.10839	1197.05350	1631.58789
2079	1453.26354	1477.78028	1209.14899	1635.44168
2080	1453.14202	1478.83379	1210.73134	1636.45450
2081	1459.07659	1483.41720	1220.87480	1636.56049
2082	1462.05658	1485.48084	1224.34410	1638.20545
2083	1460.29836	1484.90752	1225.14460	1637.73433
2084	1461.70137	1485.13874	1231.38672	1639.91671
2085	1462.70111	1483.97556	1238.34284	1639.95807
2086	1460.93981	1484.53392	1230.86386	1636.29892
2087	1462.71445	1485.67982	1227.18371	1639.42123
2088	1462.74185	1484.79385	1231.19389	1639.72448
2089	1461.62007	1484.78248	1232.61817	1639.39291
2090	1461.59350	1484.47247	1232.50622	1637.41600
2091	1463.83581	1484.97122	1236.80515	1641.14277
2092	1463.95373	1485.89601	1233.95111	1639.34018
2093	1461.84792	1484.60982	1231.05523	1638.72566
2094	1463.41850	1485.59364	1228.99176	1640.47856
2095	1464.71896	1486.52427	1237.44005	1640.83255
2096	1463.79791	1485.75974	1231.98156	1639.71838
2097	1462.48840	1485.13716	1230.70017	1639.60505
2098	1462.80770	1484.51532	1237.33662	1640.01777
2099	1463.36475	1486.17145	1234.48515	1640.35929
2100	1463.52115	1485.40003	1238.74413	1638.99829

# plot projection (with density dependence)
stoch.pop.plot <- ggplot(stoch.proj.df, aes(Year, N_projected)) + 
  geom_ribbon(aes(ymin = N_proj_lwr, ymax = N_proj_upr), 
              fill = "grey", alpha = 0.7) +
  geom_line(lwd = 1.1) + ylab("Female population (adults)") +
  theme_classic() + mythemes

stoch.pop.plot

plot(extin/interactionX, type='l', lwd=2, xlab="Years into the future", 
     main="Extinction probability for Santa Fe population")

# pop growth rate
popSGR <- stoch.growth.rate(tortoise.matrices, 
                            verbose=F,
                            prob = c(0.68, 0.16, 0.16))

lambdaCI <- list()
lambdaCI$approx <- exp(popSGR$approx)
lambdaCI$sim <- exp(popSGR$sim)
lambdaCI$sim.CI <- exp(popSGR$sim.CI)
cat('lambda\n')

## lambda

print(lambdaCI)

## $approx
## [1] 1.069908
## 
## $sim
## [1] 1.070009
## 
## $sim.CI
## [1] 1.068826 1.071194

These projections obviously do not take into account environmental stochasticity that affects tortoise vital rates (e.g., drought, ENSO cycles, temperature change, shifting sex ratios). Those information would help improve the accuracy of these projections, setting them in a more realistic future context with ongoing global change.

Let’s attach this projection figure to our other survival and abundance figures.

library(cowplot)
ggdraw() +
  draw_plot(santafe.phi.plot, x = 0, y = 0.5, width = 0.5, height = 0.5) +
  draw_plot(santafe.p.plot, x = 0.5, y = 0.5, width = 0.5, height = 0.5) +
  draw_plot(santafe.n.plot, x = 0, y = 0, width = 0.5, height = 0.5) +
  draw_plot(stoch.pop.plot, x = 0.5, y = 0, width = 0.5, height = 0.5) +
  draw_plot_label(label = c("a", "b", "c", "d"), size = 15,
                  x = c(0.08, 0.58, 0.08, 0.58), y = c(1, 1, 0.5, 0.5))

Dispersal

---

Data preparation

To assess dispersal I used the coordinates from individual tortoise capture records on Santa Fe from 2015 to 2020.

# rename santa fe data frame, remove rows without location data
movements <- santafe.data[is.na(santafe.data$Latitude) == FALSE,]
movements$Date <- paste(movements$Month, movements$Day, movements$Year, 
                        sep = "/")
movements$Date <- as.Date(movements$Date,format='%m/%d/%Y')

We should add one more column to the data frame—Days_ellapsed—to describe the time since release for each observation. But because there are three release dates, we really need three distinct groups of values for that column specific to their release cohorts.

movements2015 <- subset(movements, Cohort == "2015")
movements2017 <- subset(movements, Cohort == "2017")
movements2019 <- subset(movements, Cohort == "2019")
movementsNA <- subset(movements, is.na(Cohort))
movements2015$Days_ellapsed <- julian(movements2015$Date, 
                                      origin = as.Date("2015-06-27"))
movements2017$Days_ellapsed <- julian(movements2017$Date, 
                                      origin = as.Date("2017-04-17"))
movements2019$Days_ellapsed <- julian(movements2019$Date, 
                                      origin = as.Date("2019-02-27"))
movementsNA$Days_ellapsed <- NA
# combine them into one dataset again
movements <- rbind(movements2015, movements2017, movements2019, movementsNA)

Let’s now convert our coordinates to UTMs, calculate the distance of each point from the original release point, and make some simple plots of the study area and tortoise locations.

I’ll start by only showing the 2015 release cohort over time. Then I’ll produce the same plots including the 2017 cohort. I also need to update the UTM coordinates for the Santa Fe island shapefile so they are on the same scale as the tortoise points (relative to a central release point of 0,0).

# create shapefile
library(forcats)
library(raster)
library(rgdal)
library(sf)
library(maptools)
coordinates(object = movements) <- ~ Longitude + Latitude
proj4string(movements) <- CRS("+proj=longlat +datum=WGS84")
movements.shp <- spTransform(movements, CRSobj = CRS("+init=epsg:32715"))
movements.shp$X <- movements.shp@coords[,"Longitude"]
movements.shp$Y <- movements.shp@coords[,"Latitude"]
# Here I create new X and Y UTM fields that make coordinates relative to 
# the release point (0,0). 
# This will make it easier to quickly assess dispersal distances in the maps, 
# by centering the release point at 0,0.
movements.shp$X_corrected <- movements.shp$X - 827253
movements.shp$Y_corrected <- movements.shp$Y - 9909160
movements.data <- as.data.frame(movements.shp)
# reformat the occasion column as factor
movements.data <- movements.data %>%
  mutate(occ = as.factor(Occasion),
         occ = recode(occ, "1" = "June 2015", "2" = "August 2015", 
                      "3" = "June 2016", "4" = "April 2017", "5" = "June 2017", 
                      "6" = "June 2018", "7" = "February 2019", 
                      "8" = "April 2019", "9" = "August 2019", 
                      "10" = "March 2020")) %>% as.data.frame()

Spatial patterns - recapture data

library(sp)
santafe.shp <- readOGR("data/Santa_Fe.shp", verbose=FALSE)
santafe.shp <- spTransform(santafe.shp, CRS("+init=epsg:32715"))
santafe <- fortify(santafe.shp)
santafe$X <- santafe$long - 827253
santafe$Y <- santafe$lat - 9909160

Here is the code to make dispersal maps for specific occasions and cohorts. I’ll make plots for the first release cohorts and the total population.

First let’s look at the general distribution, showing tortoise locations at each occasion with overlayed 95% confidence ellipses.

library(ggsn)
disp.scatter <- function(data, occasion, cohort){
  ggplot(data = data[data$occ == occasion & data$Cohort == cohort,], 
         aes(x = X_corrected, y = Y_corrected)) +
    geom_polygon(inherit.aes = FALSE, data = santafe, 
                 aes(x = santafe$X, y = santafe$Y), fill = "grey") +
    geom_point(shape = 16, alpha = 0.5) +
    geom_point(inherit.aes = FALSE, aes(x = 0, y = 0), 
               shape = 4, size = 1, stroke = 1.5, color = "red") +
    stat_ellipse(aes(x = X_corrected, y = Y_corrected), color = "blue", 
                 level = 0.95, lwd = 0.9) +
    theme_classic() + mythemes + coord_equal() + theme(legend.position="none") + 
    labs(x = "Distance from release (m)", y = "Distance from release (m)") +
    annotate("text", x = 3500, y = 2200, label = "N", size = 8) +
    annotate("text", x = 3500, y = 1600, label = "\u2191", size = 15)
}

stat.ellipse.area <- function(plot){
 # Get ellipse coordinates from plot 
 # (from StackOverflow: https://tinyurl.com/yaulv58n)
  pb = ggplot_build(plot)
  el = pb$data[[4]][c("x","y")]
  # Center of ellipse
  ctr = MASS::cov.trob(el)$center 
  # Calculate distance to center from each point on the ellipse
  dist2center <- sqrt(rowSums((t(t(el)-ctr))^2))
  # Calculate area of ellipse from semi-major and semi-minor axes. 
  # These are, respectively, the largest and smallest values of dist2center. 
  return(pi*min(dist2center)*max(dist2center)/10000) # area in hectares of ellipse
}

p1 <- disp.scatter(movements.data, "June 2016", "2015")
p2 <- disp.scatter(movements.data, "June 2017", "2015")
p3 <- disp.scatter(movements.data, "June 2018", "2015")
p4 <- disp.scatter(movements.data, "August 2019", "2015")

# first cohort spread
first.cohort.spread <- data.frame(
  year = c(2016:2019),
  area = c(stat.ellipse.area(p1),stat.ellipse.area(p2),
           stat.ellipse.area(p3),stat.ellipse.area(p4)),
  prop.island = c(stat.ellipse.area(p1)/2473,stat.ellipse.area(p2)/2473,
                  stat.ellipse.area(p3)/2473,stat.ellipse.area(p4)/2473)
)

p1 <- p1 + 
  annotate("text", x = 0, y = 1800, 
           label = paste(round(first.cohort.spread$area[1], 1), " ha (",
                         round(first.cohort.spread$prop.island[1]*100, 1), "%)", 
                         sep = ""), size = 5)
p2 <- p2 + 
  annotate("text", x = 0, y = 1800, 
           label = paste(round(first.cohort.spread$area[2], 1), " ha (",
                         round(first.cohort.spread$prop.island[2]*100, 1), "%)", 
                         sep = ""), size = 5)
p3 <- p3 + 
  annotate("text", x = 0, y = 1800, 
           label = paste(round(first.cohort.spread$area[3], 1), " ha (",
                         round(first.cohort.spread$prop.island[3]*100, 1), "%)", 
                         sep = ""), size = 5)
p4 <- p4 + 
  annotate("text", x = 0, y = 1800, 
           label = paste(round(first.cohort.spread$area[4], 1), " ha (",
                         round(first.cohort.spread$prop.island[4]*100, 1), "%)", 
                         sep = ""), size = 5)

plot_grid(p1, p2, p3, p4,
          ncol  = 2, 
          labels = c("1 year", "2 years", "3 years", "4 years"), 
          label_size = 20)

The first cohort is slowly spreading over the center of the island and seems to be doubling in area almost every year since release.

Let’s see what these movements look like for the 2015 cohort when you connect the observations of individual tortoises over time as traces.

traces1 <- ggplot() +
  geom_polygon(data = santafe, 
               aes(x = santafe$X, y = santafe$Y), fill = "grey") +
  geom_path(data = movements.data[movements.data$Cohort == "2015",], 
            aes(x = X_corrected, 
                y = Y_corrected, group = PIT_final), alpha = 0.2, lwd = 0.6) +
  geom_point(aes(x = 0, y = 0), 
             shape = 4, size = 2, stroke = 1.5, color = "red") +
  theme_classic() + mythemes + coord_equal() + 
  labs(x = "Distance from release (m)", y = "Distance from release (m)", 
       title = "2015 cohort (4.5 years)", subtitle = "", caption = "") +
  annotate("text", x = 3500, y = 2200, label = "N", size = 8) +
  annotate("text", x = 3500, y = 1600, label = "\u2191", size = 15)

traces1

Individual tortoise dispersal routes from first release cohort on Santa Fe island (2015-2020)

Let’s now look at all the traces of all cohorts together.

all.traces <-
  ggplot(data = movements.data,
                  aes(x = X_corrected, y = Y_corrected)) +
  geom_polygon(data = santafe, 
               aes(x = santafe$X, y = santafe$Y), fill = "grey") +
  geom_path(aes(group = PIT_final), alpha = 0.2, lwd = 0.6) +
  geom_point(aes(x = 0, y = 0), 
             shape = 4, size = 2, stroke = 1.5, color = "red") +
  theme_classic() + mythemes + coord_equal() +
  labs(x = "Distance from release (m)", y = "Distance from release (m)") +
  annotate("text", x = 3500, y = 2200, label = "N", size = 8) +
  annotate("text", x = 3500, y = 1600, label = "\u2191", size = 15)+
  theme(plot.margin = unit(c(0,0,0,0), "mm"))

all.traces

Individual tortoise dispersal routes on Santa Fe island (2015-2020)

Interesting how tortoise movement has not been one directional. Many tortoises make large outward movements after release, only to return close to the center of the island on another occasion. These are only snapshops, so we really can’t say much about tortoise movement or dispersal from these traces, other than that tortoises seem to be exploratory in these initial post-release movements.

Finally, let’s look at dispersal ellipses for the whole tortoise population from the last survey occasion in 2020.

p.final.cohorts <-   
  ggplot(data = movements.data[movements.data$occ == "March 2020" & 
                                   !is.na(movements.data$Cohort),], 
         aes(x = X_corrected, y = Y_corrected)) +
  geom_polygon(inherit.aes = FALSE, data = santafe, 
               aes(x = santafe$X, y = santafe$Y), fill = "grey") +
  geom_point(shape = 16, alpha = 0.5) +
  geom_point(inherit.aes = FALSE, aes(x = 0, y = 0), 
             shape = 4, size = 2, stroke = 1.5, color = "red") +
  stat_ellipse(aes(x = X_corrected, y = Y_corrected, color = Cohort),
               level = 0.95, lwd = 0.9) + 
  scale_y_continuous(limits = c(-2100, 3100), breaks = seq(-2000, 2000, 1000)) +
  scale_color_manual(values = c("#E69F00", "#56B4E9", "#009E73")) +
  theme_classic() + mythemes + coord_equal() + theme(legend.position="top") + 
  labs(x = "Distance from release (m)", y = "Distance from release (m)") +
  annotate("text", x = 3500, y = 2200, label = "N", size = 8) +
  annotate("text", x = 3500, y = 1600, label = "\u2191", size = 15) +
  theme(plot.margin = unit(c(0.1, 0.1, 0.1, 0.1), "cm"))

# Get ellipse coordinates from plot 
# (from StackOverflow: https://tinyurl.com/yaulv58n)
pb <- ggplot_build(p.final.cohorts)
cohort.areas <- NULL
for(group in unique(pb$data[[4]]$group)){
  el = pb$data[[4]]
  el.group = el[el$group == group,]
  el.group.xy = el.group[c("x","y")]
  # Center of ellipse
  ctr = MASS::cov.trob(el.group.xy)$center 
  # Calculate distance to center from each point on the ellipse
  dist2center <- sqrt(rowSums((t(t(el.group.xy)-ctr))^2))
  # Calculate area of ellipse from semi-major and semi-minor axes. 
  # These are, respectively, the largest and smallest values of dist2center. 
  area_ha <- pi*min(dist2center)*max(dist2center)/10000
  dat <- data.frame(cohort = group,
                    color = el.group$colour,
                    area_ha = area_ha,
                    area_perc = area_ha/2473 * 100,
                    stringsAsFactors = FALSE)
  cohort.areas <- bind_rows(cohort.areas, dat)
}

p.final.cohorts <- 
  p.final.cohorts + 
  annotate("text", x = -2500, y = 2700, 
           label = paste(round(cohort.areas$area_ha[cohort.areas$cohort == "1"], 
                               1), " ha (",
                         round(cohort.areas$area_perc[cohort.areas$cohort == "1"], 
                               2), "%)", sep = ""), size = 4, 
           color = cohort.areas$color[cohort.areas$cohort == "1"]) +
  annotate("text", x = 0, y = 2700, 
           label = paste(round(cohort.areas$area_ha[cohort.areas$cohort == "2"], 
                               1), " ha (",
                         round(cohort.areas$area_perc[cohort.areas$cohort == "2"], 
                               2), "%)", sep = ""), size = 4,
            color = cohort.areas$color[cohort.areas$cohort == "2"]) +
  annotate("text", x = 2500, y = 2700, 
           label = paste(round(cohort.areas$area_ha[cohort.areas$cohort == "3"], 
                               1), " ha (",
                         round(cohort.areas$area_perc[cohort.areas$cohort == "3"], 
                               2), "%)", sep = ""), size = 4,
            color = cohort.areas$color[cohort.areas$cohort == "3"]) +
  theme(plot.margin = unit(c(0,0,0,0), "mm"))

p.final.cohorts

Distribution of tortoise cohorts on Santa Fe, as of March 2020.

These final distributions seem to reinforce the “doubling” seen in the first cohort’s dispersal distances over time. The first cohort is distributed over an area roughly twice the size of the second cohort, which is also roughly twice as widespread as the third cohort.

What about the ellipse for the whole population in 2020?

p.final <- 
  ggplot(data = movements.data[movements.data$occ == "March 2020",], 
         aes(x = X_corrected, y = Y_corrected)) +
  geom_polygon(inherit.aes = FALSE, data = santafe, 
               aes(x = santafe$X, y = santafe$Y), fill = "grey") +
  geom_point(shape = 16, alpha = 0.5) +
  geom_point(inherit.aes = FALSE, aes(x = 0, y = 0), 
             shape = 4, size = 1, stroke = 1.5, color = "red") +
  stat_ellipse(aes(x = X_corrected, y = Y_corrected),
               level = 0.95, lwd = 0.9, color = "blue") +
  scale_color_manual(values = c("#E69F00", "#56B4E9", "#009E73")) +
  theme_classic() + mythemes + coord_equal() + theme(legend.position="top") + 
  labs(x = "Distance from release (m)", y = "Distance from release (m)") +
  annotate("text", x = 3500, y = 2200, label = "N", size = 8) +
  annotate("text", x = 3500, y = 1600, label = "\u2191", size = 15)

p.final + annotate("text", x = 0, y = 1800, 
                   label = paste(round(stat.ellipse.area(p.final), 1), 
                                 " ha (",
                                 round(stat.ellipse.area(p.final)/2473*100, 1), 
                                 "%)", 
                                 sep = ""), size = 5)

Let’s now examine how tortoise distributions vary over time with kernel density maps.

library(spatstat)
# create a spatstat spatial planar point pattern (ppp) object
tortoises.ppp <- as(movements.shp, "ppp")
santafe.owin <- as.owin(santafe.shp)

# merge the points to the island boundary
tortoises.santafe <- tortoises.ppp[santafe.owin]
tortoises.santafe$marks <- tortoises.santafe$marks %>%
  mutate(occ = as.factor(Occasion),
         occ = recode(occ, "1" = "June 2015", "2" = "August 2015", 
                      "3" = "June 2016", "4" = "April 2017", "5" = "June 2017", 
                      "6" = "June 2018", "7" = "February 2019", 
                      "8" = "April 2019", "9" = "August 2019", 
                      "10" = "March 2020")) %>% as.data.frame()

Here I calculate kernel density of tortoises on Santa Fe, at six time events (August 2015, June 2016, June 2017, June 2018, August 2019, and March 2020). These maps are kind of like heat maps: brighter colors/higher values indicate greater tortoise densities.

# kernel density function
den.fun <- function(ppp, res){
  den.list <- list()
  ras.list <- list()
  for(occasion in c("August 2015", "June 2016", "June 2017", 
                    "June 2018", "August 2019", "March 2020")){
    # get kernel density surface
    t <- subset.ppp(ppp, occ == occasion)
    t <- rescale(t, 100)
    den <- density.ppp(t, diggle = TRUE, sigma = bw.ppl, eps = 1)
    den$xcol <- den$xcol*100
    den$yrow <- den$yrow*100
    den$xrange <- den$xrange*100
    den$yrange <- den$yrange*100
    # convert spatstat images to raster
    ras <- raster(den)
    crs(ras) <- CRS("+init=epsg:32715")
    # add objects to lists
    den.list[[occasion]] <- den
    ras.list[[occasion]] <- ras
  }
  return(list(density = den.list, raster = ras.list))
}

den.list <- den.fun(ppp = tortoises.santafe)
tortoise.brick.raw <- brick(den.list$raster)
values(tortoise.brick.raw)[values(tortoise.brick.raw) < 0] <- 0
tortoise.brick.adj <- tortoise.brick.raw
tortoise.brick.adj.lcl <- tortoise.brick.raw
tortoise.brick.adj.ucl <- tortoise.brick.raw

# correct density for detection probability
det.seq <- list()
det.seq[["est"]] <- det.df$estimate[c(1:4,6:7)]
det.seq[["lcl"]] <- det.df$ucl[c(1:4,6:7)]
det.seq[["ucl"]] <- det.df$lcl[c(1:4,6:7)]
for(i in c(1:6)){
  values(tortoise.brick.adj[[i]]) <- 
    values(tortoise.brick.adj[[i]])/det.seq[["est"]][i]
  values(tortoise.brick.adj.lcl[[i]]) <-
    values(tortoise.brick.adj.lcl[[i]])/det.seq[["lcl"]][i]
  values(tortoise.brick.adj.ucl[[i]]) <-
    values(tortoise.brick.adj.ucl[[i]])/det.seq[["ucl"]][i]
}

# write individual rasters
for(i in names(tortoise.brick.raw)){
  writeRaster(tortoise.brick.raw[[i]], filename = 
                file.path(paste("data/tdensity/tortdenraw", i, ".tif")),
              format = "GTiff", overwrite = TRUE)
  writeRaster(tortoise.brick.adj[[i]], filename = 
                file.path(paste("data/tdensity/tortdenadj", i, ".tif")),
              format = "GTiff", overwrite = TRUE)
  writeRaster(tortoise.brick.adj.lcl[[i]], filename = 
                file.path(paste("data/tdensity/tortdenadj_lcl", i, ".tif")),
              format = "GTiff", overwrite = TRUE)
   writeRaster(tortoise.brick.adj.ucl[[i]], filename = 
                file.path(paste("data/tdensity/tortdenadj_ucl", i, ".tif")),
              format = "GTiff", overwrite = TRUE)
}
# write rasterbrick as multi-band raster
writeRaster(tortoise.brick.raw, 
            filename=file.path("data/tort_kden_raw_2015_2020.tif"), 
            format="GTiff", overwrite=TRUE)
writeRaster(tortoise.brick.adj, 
            filename=file.path("data/tort_kden_adj_2015_2020.tif"), 
            format="GTiff", overwrite=TRUE)
writeRaster(tortoise.brick.adj.lcl, 
            filename=file.path("data/tort_kden_adj_lcl_2015_2020.tif"), 
            format="GTiff", overwrite=TRUE)
writeRaster(tortoise.brick.adj.ucl, 
            filename=file.path("data/tort_kden_adj_ucl_2015_2020.tif"), 
            format="GTiff", overwrite=TRUE)

library(rasterVis)
names(tortoise.brick.adj) <- c("Y2015", "Y2016", "Y2017", 
                               "Y2018", "Y2019", "Y2020")
names(tortoise.brick.adj.lcl) <- c("Y2015", "Y2016", "Y2017", 
                                   "Y2018", "Y2019", "Y2020")
names(tortoise.brick.adj.ucl) <- c("Y2015", "Y2016", "Y2017", 
                                   "Y2018", "Y2019", "Y2020")

release.pt <- data.frame(x = 827253, y = 9909160)
coordinates(release.pt) <- ~ x + y

total.density.plots <-
  levelplot(tortoise.brick.adj, par.settings = viridisTheme, 
            scales = list(cex = 1.5),
            colorkey = list(labels = list(cex = 1.5)),
            par.strip.text = list(cex = 1.5), layout = c(3,2)) +
  layer(sp.points(release.pt, pch = 4, cex=1, col="red", alpha = 0.7))

total.density.plots

In this next composite figure I’m only showing densities for the first release cohort.

den.list <- den.fun(ppp = subset(tortoises.santafe, Cohort == "2015"))
tortoise.brick.2015 <- brick(den.list$raster)
# replace negative values with 0
values(tortoise.brick.2015)[values(tortoise.brick.2015) < 0] <- 0
# adjust estimates for imperfect detection
for(i in c(1:6)){
  values(tortoise.brick.2015[[i]]) <- 
    values(tortoise.brick.2015[[i]]) / det.seq[["est"]][i]
}
names(tortoise.brick.2015) <- c("Y2015", "Y2016", "Y2017", 
                                "Y2018", "Y2019", "Y2020")
levelplot(tortoise.brick.2015, par.settings = viridisTheme, 
          scales = list(cex = 1.5),
          colorkey = list(labels = list(cex = 1.5)),
          par.strip.text = list(cex = 1.5), layout = c(3,2),
          main = list("Dispersal of first release cohort", cex = 1.5)) +
  layer(sp.points(release.pt, pch = 4, cex=1, col="red", alpha = 0.7))

At four and a half years since release, the first release cohort is widely dispersed across several spatial clusters.

Let’s now quantify dispersal over time. In this next chunk of code and following figure I look at the kernel density estimates from dispersal distances (Euclidean distance from release point), highlighting the distances of the 50% isopleth with black lines, 95% isopleth with blue lines, and max distances with red lines for each occasion.

movements.data$dist <- sqrt((movements.data$X - 827253)^2 +
                              (movements.data$Y - 9909160)^2)
movements.data$dist[movements.data$Days_ellapsed == 0] <- 0

# density plot function
den.plot <- function(data, cohort, occasion){
  dens <- density(data[data$Cohort %in% cohort & data$occ == occasion,]$dist)
  q95 <- quantile(dens, 0.95)
  q50 <- quantile(dens, 0.50)
  ggplot(data[data$Cohort %in% cohort & data$occ == occasion,], aes(dist)) + 
    geom_density(fill = "grey") + 
    geom_segment(aes(x = q50, xend = q50, yend = 0, y = 0.0075),
                 lwd = 0.8, color = "black", 
                 arrow = arrow(length = unit(0.5, "cm"))) +
    geom_segment(aes(x = q95, xend = q95, yend = 0, y = 0.0075), 
                 lwd = 0.8, color = "blue", 
                 arrow = arrow(length = unit(0.5, "cm"))) +
    geom_segment(aes(x = max(dist), xend = max(dist), yend = 0, y = 0.0075), 
                 lwd = 0.8, color = "red", 
                 arrow = arrow(length = unit(0.5, "cm"))) +
    theme_classic() + mythemes + theme(plot.title = element_text(size = 18)) +
    scale_x_continuous(expand = c(0,0), limits = c(0,2100), 
                       breaks = seq(0,2000,250)) +
    scale_y_continuous(expand = c(0,0), limits = c(0,0.0075)) + 
    geom_rug(sides = "b", alpha= 0.5)
}

# 2015 cohort
## 2015 dispersal plot for 2015 cohort / total
p15_c15 <- den.plot(data = movements.data, cohort = "2015", 
                    occasion = "August 2015") +
  labs(title = "August 2015 (2 months)", x = NULL, y = NULL)
## 2016 dispersal plot for 2015 cohort / total
p16_c15 <- den.plot(data = movements.data, cohort = "2015", 
                    occasion = "June 2016") +
  labs(title = "June 2016 (1 year)", x = NULL, y = NULL)
## 2017 dispersal plot for 2015 cohort
p17_c15 <- den.plot(data = movements.data, cohort = "2015", 
                    occasion = "June 2017") +
  labs(title = "June 2017 (2 years)", x = NULL, y = NULL)
## 2018 dispersal plot for 2015 cohort
p18_c15 <- den.plot(data = movements.data, cohort = "2015", 
                    occasion = "June 2018") +
  labs(title = "June 2018 (3 years)", x = NULL, y = NULL)
## 2019 dispersal plot for 2015 cohort
p19_c15 <- den.plot(data = movements.data, cohort = "2015", 
                    occasion = "August 2019") +
  labs(title = "August 2019 (4 years)", x = NULL, y = NULL)
## 2020 dispersal plot for 2015 cohort
p20_c15 <- den.plot(data = movements.data, cohort = "2015", 
                    occasion = "March 2020") +
  labs(title = "March 2020 (4.5 years)", x = NULL, y = NULL)

# 2017 cohort
## 2017 dispersal plot for 2017 cohort
p17_c17 <- den.plot(data = movements.data, cohort = "2017", 
                    occasion = "June 2017") +
  labs(title = "June 2017 (2 months)", x = NULL, y = NULL)
## 2018 dispersal plot for 2017 cohort
p18_c17 <- den.plot(data = movements.data, cohort = "2017", 
                    occasion = "June 2018") +
  labs(title = "June 2018 (1 year)", x = NULL, y = NULL)
## 2019 dispersal plot for 2017 cohort
p19_c17 <- den.plot(data = movements.data, cohort = "2017", 
                    occasion = "August 2019") +
  labs(title = "August 2019 (2 years)", x = NULL, y = NULL)
## 2020 dispersal plot for 2017 cohort
p20_c17 <- den.plot(data = movements.data, cohort = "2017", 
                    occasion = "March 2020") +
  labs(title = "March 2020 (2.75 years)", x = NULL, y = NULL)

# total
## 2015 dispersal plot for total
p15 <- den.plot(data = movements.data, cohort = "2015", occasion = "August 2015") +
  labs(title="August 2015",x=NULL, y = NULL)
## 2016 dispersal plot for total
p16 <- den.plot(data = movements.data, cohort = "2015", occasion = "June 2016") +
  labs(title="June 2016",x=NULL, y = NULL)
## 2017 dispersal plot for total
p17 <- den.plot(data = movements.data, cohort = c("2015", "2017"), 
                occasion = "June 2017") +
  labs(title="June 2017",x=NULL, y = NULL)
## 2018 dispersal plot for total
p18 <- den.plot(data = movements.data, cohort = c("2015", "2017"), 
                occasion = "June 2018") +
  labs(title="June 2018",x=NULL, y = NULL)
## 2019 dispersal plot for total
p19 <- den.plot(data = movements.data, cohort = c("2015", "2017", "2019"), 
                occasion = "August 2019") + labs(title="August 2019",
                                                 x=NULL, y = NULL)
## 2020 dispersal plot for total
p20 <- den.plot(data = movements.data, cohort = c("2015", "2017", "2019"), 
                occasion = "March 2020") + labs(title="March 2020",
                                                x=NULL, y = NULL)

# 2015 cohort dispersal plot
dispersal_15cohort <- ggarrange(p15_c15, p16_c15, p17_c15, 
                                p18_c15, p19_c15, p20_c15,
                                ncol = 1, nrow = 6)
annotate_figure(dispersal_15cohort,
                top = text_grob("2015 cohort dispersal", 
                                color = "black",size = 20),
                left = text_grob("Density", color = "black", 
                                 size = 18, rot = 90),
                bottom = text_grob("Distance from release (m)", 
                                   color = "black", size = 18))

# 2017 cohort dispersal plot
dispersal_17cohort <- ggarrange(p17_c17, p18_c17, p19_c17, p20_c17, 
                                ncol = 1, nrow = 4)

annotate_figure(dispersal_17cohort,
                top = text_grob("2017 cohort dispersal", 
                                color = "black",size = 20),
                left = text_grob("Density", color = "black", 
                                 size = 18, rot = 90),
                bottom = text_grob("Distance from release (m)", 
                                   color = "black", size = 18))

# Total disperal plot
dispersal_total <- ggarrange(p15, p16, p17, p18, p19, p20, ncol = 1, nrow = 6)

annotate_figure(dispersal_total,
                top = text_grob("Total dispersal (all cohorts)", 
                                color = "black",size = 20),
                left = text_grob("Density", color = "black", 
                                 size = 18, rot = 90),
                bottom = text_grob("Distance from release (m)", 
                                   color = "black", size = 18))

Let’s make this previous visualization another way using ridgeplots. I’ll align these dispersal surfaces with the population size on Santa Fe.

library(ggridges)
library(purrr)
# cumulative N plot
total_pop %>%
  map_df(rev) %>%
  ggplot(aes(x = Year, y = N_hat)) +
  scale_x_reverse() +
  geom_line(lwd = 1) +
  geom_ribbon(aes(x = Year, ymin = 0, ymax = N_hat), fill = "grey") +
  coord_flip() + scale_y_continuous(limits = c(0,600), breaks = c(0,250,500)) +
  scale_x_reverse(limits = c(2020.4, 2014.3), breaks = c(2015:2020)) +
  theme_bw() + mythemes + xlab("Year") + ylab("N-est") -> N.plot

movements.data %>%
  filter(Days_ellapsed > 0 & occ != "April 2019") %>%
  droplevels() %>%
  ggplot(aes(x = dist, y = fct_rev(occ))) +
  stat_density_ridges(quantile_lines = TRUE, quantiles = 2,
                      rel_min_height = 0.01, jittered_points = TRUE,
                      position = position_points_jitter(width = 0.5, height = 0),
                      point_shape = "|", point_size = 1,
                      alpha = 0.7, vline_size = 0.8, vline_color = "blue") +
  theme_bw() + mythemes +
  scale_x_continuous(expand = c(0.02,0), limits = c(0,2000), breaks = seq(0,2000,250)) +
  theme(axis.title.y=element_blank(),
        axis.text.y=element_blank(),
        axis.ticks.y=element_blank()) +
  annotate("text", x = 1500, y = 1.3, label = "March 2020") +
  annotate("text", x = 1500, y = 2.3, label = "August 2019") +
  annotate("text", x = 1500, y = 3.3, label = "June 2018") +
  annotate("text", x = 1500, y = 4.3, label = "June 2017") +
  annotate("text", x = 1500, y = 5.3, label = "June 2016") +
  annotate("text", x = 1500, y = 6.3, label = "August 2015") +
  labs(x = "Distance from release (m)", y = NULL) -> disp.plot

ggarrange(N.plot, disp.plot, widths = c(1, 4), ncol = 2)

Let’s directly contrast the initial (+2 months, +1 year, +2 years) dispersal distances between the first two release cohorts. Here I’ll show the 95% isopleth with dashed lines and the max distance with solid lines.

init.disp.contrast <- 
  movements.data[c(movements.data$Cohort == "2015" & 
                     movements.data$occ == "August 2015") |
                   c(movements.data$Cohort == "2015" & 
                       movements.data$occ == "June 2016") |
                   c(movements.data$Cohort == "2015" & 
                       movements.data$occ == "June 2017") |
                   c(movements.data$Cohort == "2017" & 
                       movements.data$occ == "June 2017") |
                   c(movements.data$Cohort == "2017" & 
                       movements.data$occ == "June 2018") |
                   c(movements.data$Cohort == "2017" & 
                       movements.data$occ == "August 2019"),] 

init.disp.contrast <- 
  init.disp.contrast[is.na(init.disp.contrast$PIT_final) == FALSE,]

init.disp.contrast$Ellapsed <- "1-2 months"
init.disp.contrast$Ellapsed[c(init.disp.contrast$Cohort == "2015" & 
                                init.disp.contrast$occ == "June 2016") |
                              c(init.disp.contrast$Cohort == "2017" &
                                  init.disp.contrast$occ == "June 2018")] <- "1 year"
init.disp.contrast$Ellapsed[c(init.disp.contrast$Cohort == "2015" &
                                init.disp.contrast$occ == "June 2017") |
                              c(init.disp.contrast$Cohort == "2017" &
                                  init.disp.contrast$occ == "August 2019")] <- "2 years"

init.disp.contrast$Ellapsed <- factor(init.disp.contrast$Ellapsed, 
                                      levels = c("1-2 months", "1 year", "2 years"))

disp.sum <- init.disp.contrast %>%
  droplevels() %>%
  group_by(Cohort, Ellapsed) %>%
  summarise(q95 = quantile(dist, 0.95, na.rm = T),
            maxdist = max(dist, na.rm = T)) %>%
  ungroup() 

levels(init.disp.contrast$Cohort) <- c("1", "2", "3")
levels(disp.sum$Cohort) <- c("1", "2")

init.disp.contrast.p <- ggplot(init.disp.contrast, aes(dist)) + 
  geom_density(aes(fill = Cohort), alpha = 0.3, lwd = 0.9) +
  geom_segment(data = disp.sum, aes(x = q95, xend = q95, yend = 0, 
                                    y = Inf, color = Cohort), 
               lwd = 0.8, lty = "dashed") +
  geom_segment(data = disp.sum, 
               aes(x = maxdist, xend = maxdist, 
                   yend = 0, y = Inf, color = Cohort), 
               lwd = 0.8, lty = "solid") +
  geom_text(data = disp.sum, 
            aes(label = floor(q95), x = q95, y = 0.0085, 
                angle = 90, color = Cohort), 
            size = 3, show.legend = FALSE) +
  geom_text(data = disp.sum, 
            aes(label = floor(maxdist), x = maxdist, y = 0.0085, 
                angle = 90, color = Cohort), 
            size = 3, show.legend = FALSE) +
  facet_grid(rows = vars(Ellapsed)) + theme_light() + mythemes +
  theme(plot.title = element_text(size = 18)) + 
  labs(y = "Density", x = "Distance from release (m)") +
  coord_cartesian(ylim = c(0, 0.0075), clip = 'off') +
  scale_x_continuous(expand = c(0.02,0), limits = c(0,1600), 
                     breaks = seq(0,1500,250)) +
  scale_y_continuous(expand = c(0,0)) +
  geom_rug(sides = "b", aes(color = Cohort), show.legend = FALSE) +
  theme(panel.spacing = unit(2, "lines")) + 
  theme(plot.margin = unit(c(2,1,1,1), "lines")) + 
  theme(strip.text = element_text(size = 13))
  
init.disp.contrast.p

A few takeaways:

1. Tortoises from all three cohorts seem to rapidly disperse within the first two months after release, and become a bit more fixed thereafter. The second cohort seems to disperse a bit more widely than the first in that initial period. This could be evidence of a density-dependent dispersal process.

2. The first cohort seemed to become spatially fixed two years post-release. This could be a natural dispersal plateau for the population on this island or be due to a sampling bias that missed individuals that were outside of the sampling zone.

Spatial patterns - telemetry data

Let’s also look at dispersal using radiotelemetry data from a sample of the 2015 cohort, tracked for two years, from release to June of 2017. I’ll prepare the data the same way I did for the recapture data.

telemetry <- read.csv("data/telemetry_clean.csv")
telemetry$Frecuencia <- as.factor(telemetry$Frecuencia)
telemetry$Date <- as.Date(telemetry$Date,format='%m-%d-%Y')
telemetry <- telemetry[,4:9]

# create extra rows for the June 2015 origin point for each tortoise
teletemp <- data.frame(Date = as.Date("2015-06-27"),
                       PIT = unique(telemetry$PIT),
                       Frecuencia = unique(telemetry$Frecuencia),
                       Latitud = -0.82076,
                       Longitud = -90.060063,
                       LC_cm = NA)

telemetry <- rbind(telemetry, teletemp)
telemetry$Days_ellapsed <- julian(telemetry$Date, 
                                  origin = as.Date("2015-06-27"))

# write to csv, make projected UTM shapefile in ArcMap
write.csv(telemetry, "data/telemetry_data_GIS.csv")

# read shapefile from ArcMap
telemetry.shp <- readOGR("data/telemetry_data_UTM2.shp")

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\Harrison\Documents\GC\Santa_Fe\Santa_Fe_Git\santa-fe\data\telemetry_data_UTM2.shp", layer: "telemetry_data_UTM2"
## with 97 features
## It has 10 fields
## Integer64 fields read as strings:  Field1 Days_ellap

# here I create new X and Y UTM fields that make coordinates relative to the release point (0,0). this will make it easier to quickly assess dispersal distances in the maps by centering the release point at 0,0.

telemetry.shp$X_corrected <- telemetry.shp$X - 827253
telemetry.shp$Y_corrected <- telemetry.shp$Y - 9909160
telemetry.data <- as.data.frame(telemetry.shp)

Now let’s look at those traces, both in aggregate and color-coded by individual.

traces.tele <- ggplot() +
  geom_polygon(data = santafe, aes(x = santafe$X, y = santafe$Y), 
               fill = "grey") +
  geom_path(data = telemetry.data, 
            aes(x = X_corrected, y = Y_corrected, group = Frecuencia), 
            alpha = 0.4, lwd = 0.6) +
  geom_point(aes(x = 0, y = 0), shape = 4, size = 2, 
             stroke = 1.5, color = "red") +
  theme_classic() + mythemes + coord_equal() +
  labs(x = "Distance from release (m)", y = "Distance from release (m)", 
       title = "", subtitle = "", caption = "") +
  annotate("text", x = 3500, y = 2200, label = "N", size = 8) +
  annotate("text", x = 3500, y = 1600, label = "\u2191", size = 15)

traces.tele

Let’s also look at the same figure but zoomed in and with different colors for each individual.

traces.tele.ind <- ggplot() +
  geom_polygon(data = santafe, 
               aes(x = santafe$X, y = santafe$Y), fill = "grey") +
  geom_path(data = telemetry.data, 
            aes(x = X_corrected, y = Y_corrected, 
                group = Frecuencia, color = Frecuencia), lwd = 0.8) +
  geom_point(aes(x = 0, y = 0), shape = 4, size = 2, 
             stroke = 1.5, color = "black") +
  theme_classic() + mythemes + 
  coord_equal(xlim = c(-1500,1500), ylim = c(-1500, 1500)) + 
  theme(legend.position = "none") + 
  labs(x = "Distance from release (m)", y = "Distance from release (m)", 
       title = "", subtitle = "", caption = "") +
  annotate("text", x = 1400, y = 1400, label = "N", size = 8) +
  annotate("text", x = 1400, y = 1000, label = "\u2191", size = 15)

traces.tele.ind

Summary

Let’s make one final summary table of our dispersal statistics.

Summary of tortoise dispersal on Santa Fe from 2015 to 2020.

Cohort	Days since release	Median (m)	Mean (m)	SD (m)	95% isopleth (m)	Max (m)
August 2015
2015	47	141.4	148.0	107.2	322.7	800.7
June 2016
2015	368	140.7	161.1	108.4	398.7	610.4
June 2017
2015	719	180.7	304.4	307.0	1106.6	1389.1
2017	57	162.1	182.6	152.6	396.6	941.6
Total	719	164.0	231.3	241.3	788.7	1389.1
June 2018
2015	1079	326.4	393.5	296.1	1063.5	1250.2
2017	419	188.8	229.1	154.1	484.3	863.5
Total	1079	232.0	309.0	247.1	827.6	1250.2
August 2019
2015	1506	662.0	585.2	311.3	1054.9	1284.1
2017	846	288.6	366.4	247.8	819.0	1245.0
2019	165	203.0	245.2	161.6	533.4	836.0
Total	1506	310.0	386.2	273.2	902.7	1284.1
March 2020
2015	1721	482.5	577.5	421.1	1371.9	1850.5
2017	1061	347.3	456.4	402.5	1447.1	1928.6
2019	380	269.5	349.2	296.2	1070.1	1272.6
Total	1721	353.1	470.8	390.8	1322.1	1928.6

Iguana population response

Let’s examine our Santa Fe land iguana data from 2011 to 2020 to see whether the population has been affected by the tortoise introduction so far.

A male Santa Fe land iguana (Conolophus pallidus).

I’ll do this using two corroborative data sets:

1. distance sampling data from transect surveys in 2011, 2017, and 2020

2. plot counts from 2011 and 2020

Distance sampling data

Original 2011 full-island survey

Let’s first analyze our iguana population data from the full-island survey of transects conducted in 2011.

First we’ll load the iguana and covariate data and prepare it for the distance sampling models in unmarked.

# load packages 
library(unmarked) 

# load iguana data 
iguanas2011 <- read.csv("data/iguanas_distsamp_2011.csv")

# subset by sex
males2011 <- iguanas2011[iguanas2011$TYPE == "ITM",]
females2011 <- iguanas2011[iguanas2011$TYPE == "ITH",]
juveniles2011 <- iguanas2011[iguanas2011$TYPE == "ITJ",]
total2011 <- rbind(males2011, females2011, juveniles2011)

# prepare for unmarked
## male observations
dists_machos <- 
  data.frame(distance = as.numeric(as.character(males2011$DISTANCE)),  
             transect = as.factor(males2011$TRANSECT))
# add in other transects without observations
levels(dists_machos$transect) <- c(levels(dists_machos$transect),
                                   unique(iguanas2011$TRANSECT[
                                     iguanas2011$TRANSECT %notin%
                                     as.character(dists_machos$transect)]))
## female observations
dists_hembras <- 
  data.frame(distance = as.numeric(as.character(females2011$DISTANCE)),  
             transect = as.factor(females2011$TRANSECT))
# add in other transects without observations
levels(dists_hembras$transect) <- c(levels(dists_hembras$transect),
                                   unique(iguanas2011$TRANSECT[
                                     iguanas2011$TRANSECT %notin%
                                     as.character(dists_hembras$transect)]))
## juvenile observations
dists_juvs <- 
  data.frame(distance = as.numeric(as.character(juveniles2011$DISTANCE)), 
             transect = as.factor(juveniles2011$TRANSECT))
# add in other transects without observations
levels(dists_juvs$transect) <- c(levels(dists_juvs$transect),
                                   unique(iguanas2011$TRANSECT[
                                     iguanas2011$TRANSECT %notin%
                                     as.character(dists_juvs$transect)]))

## total observations
dists_all <- 
  data.frame(distance = as.numeric(as.character(total2011$DISTANCE)), 
             transect = as.factor(total2011$TRANSECT))
# add in other transects without observations
levels(dists_all$transect) <- c(levels(dists_all$transect),
                                   unique(iguanas2011$TRANSECT[
                                     iguanas2011$TRANSECT %notin%
                                     as.character(dists_all$transect)]))

# load transect covariate data
covs <- read.csv(file = "data/distsamp_covars.csv", 
                 header = TRUE, row.names="transect") %>%
  mutate(transect = rownames(.)) %>%
  as.data.frame()

Our iguana data were originally recorded at the individual-level with continuous exact distances, but distsamp() requires the data at the transect-level with observations binned by the distance intervals. So we’ll do that for each group here, truncating the data for each at the 0.975 quantile distance for each population to remove outliers (Buckland et al. 2001).

# pool males and females to find common quantile distance for all adults
dists_adults <- rbind(dists_machos, dists_hembras)
dists_adults$quantile <- q.rank(dists_adults$distance)
max.dist.adults <- min(dists_adults$distance[dists_adults$quantile >= 0.975], 
                       na.rm = T)
# all adults
dists_adults %>% arrange(transect) -> dists_adults
yDat_adults <- formatDistData(dists_adults, distCol="distance",
                              transectNameCol="transect",
                              dist.breaks=seq(0, max.dist.adults, length.out = 5))
# reorder data frame by transect order in covariate df for later integration
yDat_adults <- yDat_adults[match(covs$transect, rownames(yDat_adults)),]

# males
yDat_machos <- formatDistData(dists_machos, distCol="distance",
                              transectNameCol="transect",
                              dist.breaks=seq(0, max.dist.adults, length.out = 5))
yDat_machos <- yDat_machos[match(covs$transect, rownames(yDat_machos)),]

# females
yDat_hembras <- formatDistData(dists_hembras, distCol="distance",
                              transectNameCol="transect",
                              dist.breaks=seq(0, max.dist.adults, 
                                              length.out = 5))
yDat_hembras <- yDat_hembras[match(covs$transect, rownames(yDat_hembras)),]

# juveniles (no truncation because of the small sample)
yDat_juvs <- formatDistData(dists_juvs, distCol="distance",
                            transectNameCol="transect", 
                            dist.breaks=seq(0,9,length.out = 5))
yDat_juvs <- yDat_juvs[match(covs$transect, rownames(yDat_juvs)),]

# total
dists_all$quantile <- q.rank(dists_all$distance)
max.dist.all <- min(dists_all$distance[dists_all$quantile >= 0.975], na.rm = T)
yDat_all <- formatDistData(dists_all, distCol="distance",
                           transectNameCol="transect",
                           dist.breaks=seq(0, max.dist.all, length.out = 5))
yDat_all <- yDat_all[match(covs$transect, rownames(yDat_all)),]

Before moving on, we should check for colinearity among our covariates. Note: our covariates were linked to each transect in GIS by extending a 50m buffer around each transect (with flat ends) and calculating mean elevation, slope, and dominant vegetation type and aspect.

Let’s look at the variance inflation factors (VIFs) to see if there is any colinearity.

# get VIFs
corvif(covs[,1:4]) # no colinearity

## 
## 
## Variance inflation factors
## 
##            GVIF Df GVIF^(1/2Df)
## elev   1.153317  1     1.073926
## slope  1.122173  1     1.059326
## aspect 1.223973  3     1.034257
## veg    1.274416  1     1.128900

There doesn’t seem to be any colinearity we need to worry about here.

Now let’s create unmarked distance sampling frames – unmarkedFrameDS() – for each iguana category, pulling together the distance observations and spatial covariates and specifying the metadata for the sampling (i.e., transect length, measurement units, etc.) to make population estimates. We use these unmarkedFrame objects to run our models.

###################################### ADULTS ##################################
umf_adults <- unmarkedFrameDS(y=as.matrix(yDat_adults), 
                              siteCovs=data.frame(elev = covs$elev,
                                                  slope = covs$slope,
                                                  aspect = covs$aspect,
                                                  veg = covs$veg), 
                              survey="line", 
                              dist.breaks=seq(0,max.dist.adults,length.out = 5), 
                              tlength=rep(500, 311), unitsIn="m")
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_adults)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_adults) <- sc.s
# summary of male data
summary(umf_adults)

## unmarkedFrameDS Object
## 
## line-transect survey design
## Distance class cutpoints (m):  0 5.75 11.5 17.25 23 
## 
## 311 sites
## Maximum number of distance classes per site: 4 
## Mean number of distance classes per site: 4 
## Sites with at least one detection: 183 
## 
## Tabulation of y observations:
##    0    1    2    3    4    5    6 
## 1030  145   39   20    6    2    2 
## 
## Site-level covariates:
##       elev              slope         aspect          veg     
##  Min.   :-2.32849   Min.   :-1.5374   E: 82   Herbaceous:230  
##  1st Qu.:-0.70876   1st Qu.:-0.6595   N:118   Shrubs    : 81  
##  Median :-0.01134   Median :-0.2766   S: 93                   
##  Mean   : 0.00000   Mean   : 0.0000   W: 18                   
##  3rd Qu.: 0.68651   3rd Qu.: 0.5084                           
##  Max.   : 3.06294   Max.   : 4.6257

hist(umf_adults, xlab="distance (m)", main="Distribution of Adult Distances", 
     cex.lab=0.8, cex.axis=0.8)

###################################### MALES ###################################
# males
umf_machos <- unmarkedFrameDS(y=as.matrix(yDat_machos), 
                              siteCovs=data.frame(elev = covs$elev,
                                                  slope = covs$slope,
                                                  aspect = covs$aspect,
                                                  veg = covs$veg), 
                              survey="line", 
                              dist.breaks=seq(0,max.dist.adults,length.out = 5), 
                              tlength=rep(500, 311), unitsIn="m")
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_machos)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_machos) <- sc.s

###################################### FEMALES #################################
# females
umf_hembras <- unmarkedFrameDS(y=as.matrix(yDat_hembras), 
                              siteCovs=data.frame(elev = covs$elev,
                                                  slope = covs$slope,
                                                  aspect = covs$aspect,
                                                  veg = covs$veg), 
                              survey="line", 
                              dist.breaks=seq(0,max.dist.adults,length.out = 5), 
                              tlength=rep(500, 311), unitsIn="m")
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_hembras)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_hembras) <- sc.s

###################################### JUVENILES ###############################
# juveniles
umf_juvs <- unmarkedFrameDS(y=as.matrix(yDat_juvs), 
                            siteCovs=data.frame(elev = covs$elev,
                                                slope = covs$slope,
                                                aspect = covs$aspect,
                                                veg = covs$veg), 
                            survey="line", 
                            dist.breaks=seq(0,9,length.out = 5), 
                            tlength=rep(500, 311), unitsIn="m")
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_juvs)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_juvs) <- sc.s
# summary of juvenile data
summary(umf_juvs)

## unmarkedFrameDS Object
## 
## line-transect survey design
## Distance class cutpoints (m):  0 2.25 4.5 6.75 9 
## 
## 311 sites
## Maximum number of distance classes per site: 4 
## Mean number of distance classes per site: 4 
## Sites with at least one detection: 28 
## 
## Tabulation of y observations:
##    0    1    2 
## 1211   29    4 
## 
## Site-level covariates:
##       elev              slope         aspect          veg     
##  Min.   :-2.32849   Min.   :-1.5374   E: 82   Herbaceous:230  
##  1st Qu.:-0.70876   1st Qu.:-0.6595   N:118   Shrubs    : 81  
##  Median :-0.01134   Median :-0.2766   S: 93                   
##  Mean   : 0.00000   Mean   : 0.0000   W: 18                   
##  3rd Qu.: 0.68651   3rd Qu.: 0.5084                           
##  Max.   : 3.06294   Max.   : 4.6257

hist(umf_juvs, xlab="distance (m)", main="Distribution of Juvenile Distances", 
     cex.lab=0.8, cex.axis=0.8)

###################################### TOTAL ###################################
# total
umf_all <- unmarkedFrameDS(y=as.matrix(yDat_all), 
                           siteCovs=data.frame(elev = covs$elev,
                                               slope = covs$slope,
                                               aspect = covs$aspect,
                                               veg = covs$veg), 
                           survey="line", 
                           dist.breaks = seq(0,max.dist.all,length.out = 5), 
                           tlength=rep(500, 311), unitsIn="m")
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_all)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_all) <- sc.s
# summary of female data
summary(umf_all)

## unmarkedFrameDS Object
## 
## line-transect survey design
## Distance class cutpoints (m):  0 5.75 11.5 17.25 23 
## 
## 311 sites
## Maximum number of distance classes per site: 4 
## Mean number of distance classes per site: 4 
## Sites with at least one detection: 189 
## 
## Tabulation of y observations:
##    0    1    2    3    4    5    6    8 
## 1021  138   49   22   10    2    1    1 
## 
## Site-level covariates:
##       elev              slope         aspect          veg     
##  Min.   :-2.32849   Min.   :-1.5374   E: 82   Herbaceous:230  
##  1st Qu.:-0.70876   1st Qu.:-0.6595   N:118   Shrubs    : 81  
##  Median :-0.01134   Median :-0.2766   S: 93                   
##  Mean   : 0.00000   Mean   : 0.0000   W: 18                   
##  3rd Qu.: 0.68651   3rd Qu.: 0.5084                           
##  Max.   : 3.06294   Max.   : 4.6257

hist(umf_all, xlab="distance (m)", main="Distribution of Iguana Distances", 
     cex.lab=0.8, cex.axis=0.8)

   

Total iguanas

---

Let’s first build models for the full iguana population. We’ll identify the most suitable detection function for all iguanas and use that going forward for model selection.

all.hazard <- distsamp(
  ~veg 
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_all, keyfun="hazard", output="density", unitsOut="ha", rel.tol=0.001)

all.halfnorm <- distsamp(
  ~veg
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_all, keyfun="halfnorm", output="density", unitsOut="ha", rel.tol=0.001)

all.negexp <- distsamp(
  ~veg
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_all, keyfun="exp", output="density", unitsOut="ha", rel.tol=0.001)

library(AICcmodavg)
aictab(cand.set = list(all.hazard, all.halfnorm, all.negexp),
     modnames = c("hazard", "halfnorm", "negative exponential"))

## 
## Model selection based on AICc:
## 
##                       K    AICc Delta_AICc AICcWt Cum.Wt      LL
## hazard               11 1298.53       0.00   0.78   0.78 -637.83
## negative exponential 10 1301.08       2.55   0.22   1.00 -640.17
## halfnorm             10 1341.34      42.81   0.00   1.00 -660.31

The hazard function appears to be the best for our iguana data.

Let’s now run a goodness of fit test on the global iguana model to decide whether our model structure is appropriate or if we need to account for overdispersion.

fitstats <- function(fm) {
    observed <- getY(fm@data)
    expected <- fitted(fm)
    resids <- residuals(fm)
    sse <- sum(resids^2)
    chisq <- sum((observed - expected)^2 / expected, na.rm = TRUE)
    freeTuke <- sum((sqrt(observed) - sqrt(expected))^2, na.rm = TRUE)
    out <- c(SSE=sse, Chisq=chisq, freemanTukey=freeTuke)
    return(out)
}

set.seed(1)
GoF.all <- parboot(all.hazard, fitstats, nsim=1000, report=5)

## t0 = 503.3283 1498.096 255.8762

GoF.all

## 
## Call: 
## parboot(object = all.hazard, statistic = fitstats, nsim = 1000, report = 5)
## 
## Parametric Bootstrap Statistics:
##                t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)
## SSE           503          145.0             30.3        0.000
## Chisq        1498          270.1            107.5        0.023
## freemanTukey  256           36.8             11.0        0.000
## 
## t_B quantiles:
##               0% 2.5%  25%  50%  75% 97.5% 100%
## SSE          273  303  338  357  379   425  455
## Chisq        913 1055 1153 1218 1291  1483 1646
## freemanTukey 188  199  211  219  227   241  254
## 
## t0 = Original statistic computed from data
## t_B = Vector of bootstrap samples

par(mfrow = c(3,1))
plot(GoF.all)

c.hat.all <- GoF.all@t0[2] / mean(GoF.all@t.star[,2]); c.hat.all

##    Chisq 
## 1.219923

Our global model has some issues with goodness of fit. The c-hat value is acceptable, but the model performs poorly on all three goodness of fit tests. Let’s see if using a negative binomial distribution improves the model fit with gdistsamp.

In this case, we won’t fit anything for phi (just the intercept), which is the availability parameter.

umf_all_g <- unmarkedFrameGDS(y=as.matrix(yDat_all), 
                              siteCovs=data.frame(elev = covs$elev,
                                                  slope = covs$slope,
                                                  aspect = covs$aspect,
                                                  veg = covs$veg), 
                              survey="line", 
                              dist.breaks=seq(0,max.dist.all,length.out = 5), 
                              tlength=rep(500, 311), unitsIn="m", numPrimary = 1)
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_all_g)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_all_g) <- sc.s

all.hazard.nb <- gdistsamp(
  ~elev+I(elev^2)+slope+aspect+veg, 
  ~1, 
  ~veg,
  mixture = "NB",
  umf_all_g, keyfun="hazard", output="density", unitsOut="ha", rel.tol=0.001)

set.seed(1)
GoF.all.nb <- parboot(all.hazard.nb, fitstats, nsim=1000, report=5)

## t0 = 613.4983 3716.53 211.1958

GoF.all.nb

## 
## Call: 
## parboot(object = all.hazard.nb, statistic = fitstats, nsim = 1000, report = 5)
## 
## Parametric Bootstrap Statistics:
##                t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)
## SSE           613          26.80             69.9        0.325
## Chisq        3717         312.72            287.9        0.126
## freemanTukey  211           7.12             10.7        0.252
## 
## t_B quantiles:
##                0% 2.5%  25%  50%  75% 97.5% 100%
## SSE           407  461  537  582  631   731  900
## Chisq        2576 2943 3211 3371 3557  4067 5424
## freemanTukey  174  184  197  203  211   224  243
## 
## t0 = Original statistic computed from data
## t_B = Vector of bootstrap samples

par(mfrow = c(3,1))
plot(GoF.all.nb)

c.hat.all.nb <- GoF.all.nb@t0[2] / mean(GoF.all.nb@t.star[,2]); c.hat.all.nb

##    Chisq 
## 1.091874

The negative binomial abundance model yields a much better model fit, so let’s stick with this for all our iguana model groups.

We will use the following candidate model list for all iguana groups.

all <- list() # make a list to store macho models
all$null <- gdistsamp(lambdaformula = ~1,
                         phiformula = ~1, 
                         pformula = ~1, 
                         umf_all_g, mixture = "NB",
                         keyfun="hazard", output="density", unitsOut="ha")

all$elev <- gdistsamp(lambdaformula = ~elev, 
                         phiformula = ~1, 
                         pformula = ~1, 
                         umf_all_g, mixture = "NB",
                         keyfun="hazard", output="density", unitsOut="ha")

all$elev2 <- gdistsamp(lambdaformula = ~elev+I(elev^2), 
                          phiformula = ~1, 
                          pformula = ~1, 
                          umf_all_g, mixture = "NB",
                          keyfun="hazard", output="density", unitsOut="ha")

all$slope <- gdistsamp(lambdaformula = ~slope,  
                          phiformula = ~1, 
                          pformula = ~1,
                          umf_all_g, mixture = "NB",
                          keyfun="hazard", output="density", unitsOut="ha")

all$aspect <- gdistsamp(lambdaformula = ~aspect, 
                           phiformula = ~1, 
                           pformula = ~1, 
                           umf_all_g, mixture = "NB",
                           keyfun="hazard", output="density", unitsOut="ha")

all$veg <- gdistsamp(lambdaformula = ~veg, 
                        phiformula = ~1, 
                        pformula = ~1, 
                        umf_all_g, mixture = "NB",
                        keyfun="hazard", output="density", unitsOut="ha")

all$topo <- gdistsamp(lambdaformula = ~elev+slope+aspect, 
                         phiformula = ~1, 
                         pformula = ~1, 
                         umf_all_g, mixture = "NB",
                         keyfun="hazard", output="density", unitsOut="ha")

all$topo2 <- gdistsamp(lambdaformula = ~elev+I(elev^2)+slope+aspect, 
                          phiformula = ~1, 
                          pformula = ~1, 
                          umf_all_g, mixture = "NB",
                          keyfun="hazard", output="density", unitsOut="ha")

all$subglobal <- gdistsamp(lambdaformula = ~elev+slope+aspect+veg, 
                              phiformula = ~1, 
                              pformula = ~1, 
                              umf_all_g, mixture = "NB",
                              keyfun="hazard", output="density", unitsOut="ha")

all$global <- gdistsamp(lambdaformula = ~elev+I(elev^2)+slope+aspect+veg, 
                           phiformula = ~1, 
                           pformula = ~1, 
                           umf_all_g, mixture = "NB",
                           keyfun="hazard", output="density", unitsOut="ha")

all$p.null <- gdistsamp(lambdaformula = ~1, 
                           phiformula = ~1, 
                           pformula = ~veg, 
                           umf_all_g, mixture = "NB",
                           keyfun="hazard", output="density", unitsOut="ha")

all$p.elev <- gdistsamp(lambdaformula = ~elev, 
                           phiformula = ~1, 
                           pformula = ~veg, 
                           umf_all_g, mixture = "NB",
                           keyfun="hazard", output="density", unitsOut="ha")

all$p.elev2 <- gdistsamp(lambdaformula = ~elev+I(elev^2), 
                            phiformula = ~1, 
                            pformula = ~veg, 
                            umf_all_g, mixture = "NB",
                            keyfun="hazard", output="density", unitsOut="ha")

all$p.slope <- gdistsamp(lambdaformula = ~slope, 
                            phiformula = ~1, 
                            pformula = ~veg, 
                            umf_all_g, mixture = "NB",
                            keyfun="hazard", output="density", unitsOut="ha")

all$p.aspect <- gdistsamp(lambdaformula = ~aspect, 
                             phiformula = ~1, 
                             pformula = ~veg, 
                             umf_all_g, mixture = "NB",
                             keyfun="hazard", output="density", unitsOut="ha")

all$p.veg <- gdistsamp(lambdaformula = ~veg, 
                          phiformula = ~1, 
                          pformula = ~veg, 
                          umf_all_g, mixture = "NB",
                          keyfun="hazard", output="density", unitsOut="ha")

all$p.topo <- gdistsamp(lambdaformula = ~elev+slope+aspect, 
                           phiformula = ~1, 
                           pformula = ~veg, 
                           umf_all_g, mixture = "NB",
                           keyfun="hazard", output="density", unitsOut="ha")

all$p.topo2 <- gdistsamp(lambdaformula = ~elev+I(elev^2)+slope+aspect, 
                            phiformula = ~1, 
                            pformula = ~veg, 
                            umf_all_g, mixture = "NB",
                            keyfun="hazard", output="density", unitsOut="ha")

all$p.subglobal <- gdistsamp(lambdaformula = ~elev+slope+aspect+veg, 
                                phiformula = ~1, 
                                pformula = ~veg, 
                                umf_all_g, mixture = "NB",
                                keyfun="hazard", output="density", unitsOut="ha")

all$p.global <- gdistsamp(lambdaformula = ~elev+I(elev^2)+slope+aspect+veg, 
                             phiformula = ~1, 
                             pformula = ~veg, 
                             umf_all_g, mixture = "NB",
                             keyfun="hazard", output="density", unitsOut="ha")

# Making a QAIC table - list of all models for ranking
library(AICcmodavg)
# make custom model names showing the variables
modnames <- c("lambda(.) p(.)", 
              "lambda(elev) p(.)", 
              "lambda(elev + elev^2^) p(.)",
              "lambda(slope) p(.)", 
              "lambda(aspect) p(.)",
              "lambda(veg) p(.)", 
              "lambda(elev + slope + aspect) p(.)", 
              "lambda(elev + elev^2^ + slope + aspect) p(.)",
              "lambda(elev + slope + aspect + veg) p(.)", 
              "lambda(elev + elev^2^ + slope + aspect + veg) p(.)", 
              "lambda(.) p(veg)", 
              "lambda(elev) p(veg)", 
              "lambda(elev + elev^2^) p(veg)",
              "lambda(slope) p(veg)", 
              "lambda(aspect) p(veg)", 
              "lambda(veg) p(veg)", 
              "lambda(elev + slope + aspect) p(veg)",
              "lambda(elev + elev^2^ + slope + aspect) p(veg)",
              "lambda(elev + slope + aspect + veg) p(veg)",
              "lambda(elev + elev^2^ + slope + aspect + veg) p(veg)")

# Rank by QAIC and print 
all.rankings <- as.data.frame(aictab(cand.set = all, 
                                        modnames = modnames,
                                        c.hat = c.hat.all.nb, second.ord = FALSE, 
                                        sort = TRUE))

all.rankings$Deviance <- round(-2*all.rankings$Quasi.LL,2) # get deviances
all.rankings <- all.rankings[,c(1,2,4,6,9,10)]
colnames(all.rankings) <- c("Model", "K", "Delta_QAIC", 
                               "QAIC_wt.", "Cum. weight", "Deviance")

kable(all.rankings, "html", row.names = FALSE, 
      caption = "Poisson abundance model rankings for total iguanas", 
      digits = 3) %>% 
  kable_styling(bootstrap_options = c("striped", "condensed")) %>%
  scroll_box(height = "350px")

Poisson abundance model rankings for total iguanas

Model	K	Delta_QAIC	QAIC_wt.	Cum. weight	Deviance
lambda(aspect) p(veg)	9	0.000	0.550	0.550	909.49
lambda(elev + elev2 + slope + aspect) p(veg)	12	2.296	0.175	0.725	905.78
lambda(elev + slope + aspect) p(veg)	11	3.655	0.089	0.814	909.14
lambda(elev + elev2 + slope + aspect + veg) p(veg)	13	4.173	0.068	0.882	905.66
lambda(elev + slope + aspect + veg) p(veg)	12	5.574	0.034	0.916	909.06
lambda(elev + elev2 + slope + aspect + veg) p(.)	12	5.971	0.028	0.944	909.46
lambda(aspect) p(.)	8	7.060	0.016	0.960	918.55
lambda(elev + elev2 + slope + aspect) p(.)	11	7.248	0.015	0.974	912.73
lambda(elev + slope + aspect + veg) p(.)	11	7.371	0.014	0.988	912.86
lambda(elev + slope + aspect) p(.)	10	9.014	0.006	0.994	916.50
lambda(.) p(veg)	6	11.649	0.002	0.996	927.14
lambda(elev + elev2) p(veg)	8	12.347	0.001	0.997	923.83
lambda(elev) p(veg)	7	13.230	0.001	0.998	926.72
lambda(veg) p(veg)	7	13.433	0.001	0.998	926.92
lambda(slope) p(veg)	7	13.649	0.001	0.999	927.14
lambda(elev + elev2) p(.)	7	15.050	0.000	0.999	928.54
lambda(veg) p(.)	6	15.230	0.000	1.000	930.72
lambda(.) p(.)	5	16.463	0.000	1.000	933.95
lambda(elev) p(.)	6	16.610	0.000	1.000	932.10
lambda(slope) p(.)	6	18.327	0.000	1.000	933.81

write.csv(all.rankings, "data/iguana_all_QAIC.csv")

It seems like aspect is overwhelmingly driving iguana distributions, with more iguanas in areas with north and west-facing slopes. There is still some model uncertainty, with several other models within 6 QAIC units and a cumulative weight of 0.95.

Let’s follow the same approach for all our iguana subgroups. I don’t show all the code for these sections, as they will be virtually the same as what was presented above.

Male and female adult iguanas should display the same detection function, so let’s examine goodness of fit on a pooled adult dataset rather than each sex individually.

adults.hazard <- distsamp(
  ~veg 
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_adults, keyfun="hazard", output="density", unitsOut="ha", rel.tol=0.0001)

adults.halfnorm <- distsamp(
  ~veg
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_adults, keyfun="halfnorm", output="density", unitsOut="ha", rel.tol=0.0001)

adults.negexp <- distsamp(
  ~veg
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_adults, keyfun="exp", output="density", unitsOut="ha", rel.tol=0.0001)

aictab(cand.set = list(adults.hazard, adults.halfnorm, adults.negexp),
     modnames = c("hazard", "halfnorm", "negative exponential"))

## 
## Model selection based on AICc:
## 
##                       K    AICc Delta_AICc AICcWt Cum.Wt      LL
## hazard               11 1221.68       0.00   0.81   0.81 -599.40
## negative exponential 10 1224.63       2.95   0.19   1.00 -601.95
## halfnorm             10 1262.43      40.75   0.00   1.00 -620.85

The hazard function again is what we probably want. Let’s examine goodness of fit.

set.seed(12)
GoF.adults <- parboot(adults.hazard, fitstats, nsim=1000, report=5)

## t0 = 426.3899 1491.163 238.4203

GoF.adults

## 
## Call: 
## parboot(object = adults.hazard, statistic = fitstats, nsim = 1000, report = 5)
## 
## Parametric Bootstrap Statistics:
##                t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)
## SSE           426          104.0             29.4     0.000999
## Chisq        1491          -60.6          10101.4     0.028971
## freemanTukey  238           25.4             10.8     0.008991
## 
## t_B quantiles:
##               0% 2.5%  25%  50%  75% 97.5%   100%
## SSE          250  269  301  320  342   386    439
## Chisq        965 1037 1148 1219 1292  1525 320642
## freemanTukey 181  193  206  213  221   234    249
## 
## t0 = Original statistic computed from data
## t_B = Vector of bootstrap samples

par(mfrow = c(3,1))
plot(GoF.adults)

c.hat.adults <- GoF.adults@t0[2] / mean(GoF.adults@t.star[,2]); c.hat.adults

##     Chisq 
## 0.9609336

Let’s look at the negative binomial global hazard model fit statistics for adults.

umf_adults_g <- unmarkedFrameGDS(y=as.matrix(yDat_adults), 
                                 siteCovs=data.frame(elev = covs$elev,
                                                     slope = covs$slope,
                                                     aspect = covs$aspect,
                                                     veg = covs$veg), 
                                 survey="line", 
                                 dist.breaks=seq(0, max.dist.adults,
                                                 length.out = 5), 
                                 tlength=rep(500, 311), 
                                 unitsIn="m", 
                                 numPrimary = 1)
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_adults_g)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_adults_g) <- sc.s

adults.hazard.nb <- gdistsamp(
  ~elev+I(elev^2)+slope+aspect+veg, 
  ~1, 
  ~veg,
  mixture = "NB",
  umf_adults_g, keyfun="hazard", output="density", unitsOut="ha", rel.tol=0.001)

set.seed(1)
GoF.adults.nb <- parboot(adults.hazard.nb, fitstats, nsim=1000, report=5)

## t0 = 515.4821 3670.65 195.402

GoF.adults.nb

## 
## Call: 
## parboot(object = adults.hazard.nb, statistic = fitstats, nsim = 1000, report = 5)
## 
## Parametric Bootstrap Statistics:
##                t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)
## SSE           515          20.70            57.44        0.339
## Chisq        3671         360.17           310.24        0.112
## freemanTukey  195           4.33             9.93        0.326
## 
## t_B quantiles:
##                0% 2.5%  25%  50%  75% 97.5% 100%
## SSE           330  396  452  492  532   613  717
## Chisq        2516 2845 3110 3262 3451  4024 5663
## freemanTukey  159  173  184  191  198   211  220
## 
## t0 = Original statistic computed from data
## t_B = Vector of bootstrap samples

par(mfrow = c(3,1))
plot(GoF.adults.nb)

c.hat.adults.nb <- GoF.adults.nb@t0[2] / mean(GoF.adults.nb@t.star[,2]) 
c.hat.adults.nb

##    Chisq 
## 1.108797

This model fits the goodness of fit tests, with minimal additional overdispersion. Let’s compare models for male and female iguanas using this distribution and c-hat correction.    

Male iguanas

---

First we need to create a new unmarkedFrameGDS for male iguanas.

umf_machos_g <- unmarkedFrameGDS(y=as.matrix(yDat_machos), 
                                 siteCovs=data.frame(elev = covs$elev,
                                                     slope = covs$slope,
                                                     aspect = covs$aspect,
                                                     veg = covs$veg), 
                                 survey="line", 
                                 dist.breaks=seq(0, max.dist.adults,
                                                 length.out = 5), 
                                 tlength=rep(500, 311), 
                                 unitsIn="m", 
                                 numPrimary = 1)
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_machos_g)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_machos_g) <- sc.s

Now let’s build and rank our candidate model suite for male iguanas.

Poisson abundance model rankings for male iguanas

Model	K	Delta_QAIC	QAIC_wt.	Cum. weight	Deviance
lambda(aspect) p(veg)	9	0.000	0.529	0.529	651.76
lambda(elev + elev2 + slope + aspect) p(veg)	12	2.502	0.151	0.681	648.26
lambda(elev + slope + aspect) p(veg)	11	3.204	0.107	0.787	650.96
lambda(elev + elev2 + slope + aspect + veg) p(veg)	13	4.500	0.056	0.843	648.26
lambda(elev + elev2 + slope + aspect + veg) p(.)	12	4.812	0.048	0.891	650.57
lambda(elev + slope + aspect + veg) p(veg)	12	5.195	0.039	0.930	650.96
lambda(elev + slope + aspect + veg) p(.)	11	5.507	0.034	0.964	653.27
lambda(.) p(veg)	6	8.709	0.007	0.971	666.47
lambda(elev + elev2) p(veg)	8	8.890	0.006	0.977	662.65
lambda(elev + elev2 + slope + aspect) p(.)	11	9.373	0.005	0.982	657.13
lambda(elev) p(veg)	7	9.681	0.004	0.986	665.44
lambda(aspect) p(.)	8	10.158	0.003	0.989	663.92
lambda(elev + slope + aspect) p(.)	10	10.569	0.003	0.992	660.33
lambda(slope) p(veg)	7	10.707	0.003	0.994	666.47
lambda(veg) p(veg)	7	10.708	0.003	0.997	666.47
lambda(veg) p(.)	6	11.020	0.002	0.999	668.78
lambda(elev + elev2) p(.)	7	13.538	0.001	1.000	669.30
lambda(elev) p(.)	6	15.085	0.000	1.000	672.85
lambda(.) p(.)	5	16.477	0.000	1.000	676.24
lambda(slope) p(.)	6	18.255	0.000	1.000	676.02

Similar rankings to the full iguana population.

machos$p.aspect

## 
## Call:
## gdistsamp(lambdaformula = ~aspect, phiformula = ~1, pformula = ~veg, 
##     data = umf_machos_g, keyfun = "hazard", output = "density", 
##     unitsOut = "ha", mixture = "NB")
## 
## Abundance:
##             Estimate    SE      z  P(>|z|)
## (Intercept)   -0.137 0.277 -0.495 0.620377
## aspectN        0.605 0.213  2.839 0.004522
## aspectS        0.160 0.231  0.692 0.489136
## aspectW        0.988 0.290  3.409 0.000652
## 
## Detection:
##             Estimate    SE     z  P(>|z|)
## (Intercept)    1.325 0.300  4.41 1.01e-05
## vegShrubs     -0.664 0.199 -3.33 8.64e-04
## 
## Hazard-rate(scale):
##  Estimate    SE    z  P(>|z|)
##     0.993 0.223 4.45 8.71e-06
## 
## Dispersion:
##  Estimate   SE    z P(>|z|)
##      2.51 1.76 1.43   0.154
## 
## AIC: 738.671

Aspect seems to be important and vegetation type affects detection.

   

Female iguanas

---

umf_hembras_g <- unmarkedFrameGDS(y=as.matrix(yDat_hembras), 
                                 siteCovs=data.frame(elev = covs$elev,
                                                     slope = covs$slope,
                                                     aspect = covs$aspect,
                                                     veg = covs$veg), 
                                 survey="line", 
                                 dist.breaks=seq(0, max.dist.adults,
                                                 length.out = 5), 
                                 tlength=rep(500, 311), 
                                 unitsIn="m", 
                                 numPrimary = 1)
# scale continuous covariates (elevation, slope)
sc <- siteCovs(umf_hembras_g)
sc.s <- cbind(scale(sc[,1:2]), sc[,3:4])
siteCovs(umf_hembras_g) <- sc.s

Poisson abundance model rankings for female iguanas

Model	K	Delta_QAIC	QAIC_wt.	Cum. weight	Deviance
lambda(aspect) p(veg)	9	0.000	0.360	0.360	641.36
lambda(aspect) p(.)	8	2.097	0.126	0.486	645.45
lambda(.) p(veg)	6	2.697	0.094	0.580	650.05
lambda(.) p(.)	5	3.788	0.054	0.634	653.14
lambda(elev + slope + aspect) p(veg)	11	3.875	0.052	0.686	641.23
lambda(veg) p(veg)	7	4.103	0.046	0.732	649.46
lambda(slope) p(veg)	7	4.625	0.036	0.768	649.98
lambda(veg) p(.)	6	4.669	0.035	0.803	652.03
lambda(elev) p(veg)	7	4.674	0.035	0.838	650.03
lambda(elev + slope + aspect + veg) p(veg)	12	5.597	0.022	0.860	640.95
lambda(elev) p(.)	6	5.630	0.022	0.881	652.99
lambda(elev + elev2 + slope + aspect) p(veg)	12	5.761	0.020	0.901	641.12
lambda(slope) p(.)	6	5.787	0.020	0.921	653.14
lambda(elev + slope + aspect) p(.)	10	6.001	0.018	0.939	645.36
lambda(elev + slope + aspect + veg) p(.)	11	6.163	0.017	0.956	643.52
lambda(elev + elev2) p(veg)	8	6.619	0.013	0.969	649.98
lambda(elev + elev2 + slope + aspect + veg) p(veg)	13	7.469	0.009	0.978	640.83
lambda(elev + elev2) p(.)	7	7.471	0.009	0.986	652.83
lambda(elev + elev2 + slope + aspect) p(.)	11	7.804	0.007	0.994	645.16
lambda(elev + elev2 + slope + aspect + veg) p(.)	12	8.035	0.006	1.000	643.39

Similar rankings to the full iguana and male populations.

hembras$p.aspect

## 
## Call:
## gdistsamp(lambdaformula = ~aspect, phiformula = ~1, pformula = ~veg, 
##     data = umf_hembras_g, keyfun = "hazard", output = "density", 
##     unitsOut = "ha", mixture = "NB")
## 
## Abundance:
##             Estimate    SE      z P(>|z|)
## (Intercept)  -0.4377 0.303 -1.446  0.1482
## aspectN       0.5136 0.244  2.104  0.0354
## aspectS       0.0519 0.269  0.193  0.8473
## aspectW       0.8566 0.357  2.398  0.0165
## 
## Detection:
##             Estimate    SE     z  P(>|z|)
## (Intercept)    1.381 0.350  3.95 0.000079
## vegShrubs     -0.424 0.206 -2.06 0.039296
## 
## Hazard-rate(scale):
##  Estimate    SE    z  P(>|z|)
##     0.809 0.238 3.39 0.000688
## 
## Dispersion:
##  Estimate    SE    z P(>|z|)
##     0.829 0.538 1.54   0.123
## 
## AIC: 727.1347

   

Juvenile iguanas

---

Let’s now examine juvenile iguana distance sampling models.

juvs.hazard <- distsamp(
  ~veg 
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_juvs, keyfun="hazard", output="density", unitsOut="ha", rel.tol=0.0001)

juvs.halfnorm <- distsamp(
  ~veg
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_juvs, keyfun="halfnorm", output="density", unitsOut="ha", rel.tol=0.0001)

juvs.negexp <- distsamp(
  ~veg
  ~elev+I(elev^2)+slope+aspect+veg, 
  umf_juvs, keyfun="exp", output="density", unitsOut="ha", rel.tol=0.0001)

aictab(cand.set = list(juvs.hazard, juvs.halfnorm, juvs.negexp),
     modnames = c("hazard", "halfnorm", "negative exponential"))

## 
## Model selection based on AICc:
## 
##                       K   AICc Delta_AICc AICcWt Cum.Wt      LL
## halfnorm             10 334.77       0.00   0.39   0.39 -157.02
## negative exponential 10 334.89       0.12   0.37   0.77 -157.08
## hazard               11 335.82       1.05   0.23   1.00 -156.47

All three detection functions perform similarly. Let’s compare the GoF of the half normal and negative exponential functions.

set.seed(12)
GoF.juvs.hn <- parboot(juvs.halfnorm, fitstats, nsim=1000, report=5)

## t0 = 42.89105 1360.422 59.04461

GoF.juvs.hn

## 
## Call: 
## parboot(object = juvs.halfnorm, statistic = fitstats, nsim = 1000, report = 5)
## 
## Parametric Bootstrap Statistics:
##                  t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)
## SSE            42.9           6.51             6.22        0.148
## Chisq        1360.4         193.06           321.47        0.102
## freemanTukey   59.0           2.48             8.13        0.387
## 
## t_B quantiles:
##               0% 2.5%  25%  50%  75% 97.5% 100%
## SSE           19   25   32   36   40    50   59
## Chisq        690  867 1026 1122 1224  1712 5865
## freemanTukey  32   41   51   56   62    73   81
## 
## t0 = Original statistic computed from data
## t_B = Vector of bootstrap samples

par(mfrow = c(3,1))
plot(GoF.juvs.hn)

c.hat.juvs.hn <- GoF.juvs.hn@t0[2] / mean(GoF.juvs.hn@t.star[,2]); 
c.hat.juvs.hn

##    Chisq 
## 1.165383

set.seed(12)
GoF.juvs.neg <- parboot(juvs.negexp, fitstats, nsim=1000, report=5)

## t0 = 42.79944 1334.971 58.97153

GoF.juvs.neg

## 
## Call: 
## parboot(object = juvs.negexp, statistic = fitstats, nsim = 1000, report = 5)
## 
## Parametric Bootstrap Statistics:
##                  t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)
## SSE            42.8           6.43             6.25        0.147
## Chisq        1335.0         151.24           258.63        0.126
## freemanTukey   59.0           2.52             8.16        0.385
## 
## t_B quantiles:
##               0% 2.5%  25%  50%  75% 97.5% 100%
## SSE           19   26   32   36   40    49   58
## Chisq        718  907 1062 1143 1242  1820 4228
## freemanTukey  32   42   51   56   62    73   83
## 
## t0 = Original statistic computed from data
## t_B = Vector of bootstrap samples

par(mfrow = c(3,1))
plot(GoF.juvs.neg)

c.hat.juvs.neg <- GoF.juvs.neg@t0[2] / mean(GoF.juvs.neg@t.star[,2]); 
c.hat.juvs.neg

##    Chisq 
## 1.127765

The negative exponential function provides a slightly lower c-hat, so let’s go with that function.

Poisson abundance model rankings for juvenile iguanas

Model	K	Delta_QAIC	QAIC_wt.	Cum. weight	Deviance
lambda(elev + elev2) p(.)	5	0.000	0.263	0.263	283.89
lambda(elev + elev2) p(veg)	6	0.148	0.244	0.507	282.04
lambda(veg) p(.)	4	2.101	0.092	0.599	287.99
lambda(.) p(.)	3	2.288	0.084	0.683	290.18
lambda(.) p(veg)	4	2.957	0.060	0.743	288.85
lambda(slope) p(.)	4	4.048	0.035	0.777	289.94
lambda(veg) p(veg)	5	4.100	0.034	0.811	287.99
lambda(elev) p(.)	4	4.288	0.031	0.842	290.18
lambda(slope) p(veg)	5	4.552	0.027	0.869	288.44
lambda(elev + elev2 + slope + aspect) p(.)	9	4.646	0.026	0.895	280.53
lambda(elev + elev2 + slope + aspect + veg) p(.)	10	4.682	0.025	0.920	278.57
lambda(elev) p(veg)	5	4.829	0.024	0.944	288.72
lambda(elev + elev2 + slope + aspect) p(veg)	10	5.549	0.016	0.960	279.44
lambda(aspect) p(.)	6	5.749	0.015	0.975	287.64
lambda(elev + elev2 + slope + aspect + veg) p(veg)	11	6.680	0.009	0.984	278.57
lambda(aspect) p(veg)	7	7.120	0.007	0.992	287.01
lambda(elev + slope + aspect) p(.)	8	8.932	0.003	0.995	286.82
lambda(elev + slope + aspect + veg) p(.)	9	9.189	0.003	0.997	285.08
lambda(elev + slope + aspect) p(veg)	9	9.990	0.002	0.999	285.88
lambda(elev + slope + aspect + veg) p(veg)	10	11.188	0.001	1.000	285.08

We see some support for an elevation effect on juvenile iguanas. The null model is ranked close to the top though, which may be due to the limited amount of data on juvenile iguanas in this dataset. No support really for a vegetation effect on detection.

juvs$elev2

## 
## Call:
## distsamp(formula = ~1 ~ elev + I(elev^2), data = umf_juvs, keyfun = "exp", 
##     output = "density", unitsOut = "ha")
## 
## Density:
##             Estimate    SE      z P(>|z|)
## (Intercept)  -0.7720 0.297 -2.598 0.00937
## elev          0.0322 0.231  0.139 0.88925
## I(elev^2)    -0.4942 0.229 -2.160 0.03074
## 
## Detection:
##  Estimate    SE    z  P(>|z|)
##      1.41 0.302 4.67 3.02e-06
## 
## AIC: 328.1595

juvs$p.elev2

## 
## Call:
## distsamp(formula = ~veg ~ elev + I(elev^2), data = umf_juvs, 
##     keyfun = "exp", output = "density", unitsOut = "ha")
## 
## Density:
##             Estimate    SE      z P(>|z|)
## (Intercept)   -0.748 0.297 -2.515  0.0119
## elev           0.111 0.239  0.465  0.6419
## I(elev^2)     -0.512 0.231 -2.214  0.0268
## 
## Detection:
##                 Estimate    SE    z  P(>|z|)
## rate(Intercept)    1.229 0.292 4.21 2.54e-05
## ratevegShrubs      0.641 0.519 1.23 2.17e-01
## 
## AIC: 328.0714

Let’s visualize our covariate effects on each iguana group. To do this I’ll make model averaged predictions of density across values of each covariate individually, keeping the other covariates at constant values or getting the average value across factor levels for aspect and vegetation type.

library(plyr)
# 1. ELEVATION
elev.sim <- seq(min(covs$elev), max(covs$elev), length.out = 30)
elev.new <- (elev.sim - mean(covs$elev))/sd(covs$elev)
## predict function for elevation effect
elev.pred.fun <- function(mod.list, group.chat){
  pred = as.data.frame(modavgPred(cand.set = mod.list, type = "response", 
                                  parm.type = "lambda",
                                  newdata = 
                                    data.frame(elev = rep(elev.new, 8),
                                               slope = 0,
                                               aspect = c(rep("N", 60), 
                                                          rep("E", 60), 
                                                          rep("S", 60), 
                                                          rep("W", 60)), 
                                               veg = c(rep(c(rep("Shrubs", 30),
                                                             rep("Herbaceous", 30)), 
                                                           4))), 
                                  c.hat = group.chat)$matrix.output)
  pred$elev <- rep(elev.sim, 8)
  pred = ddply(pred, .(elev), summarize, 
               density.pred = mean(mod.avg.pred),
               se = mean(uncond.se),
               lcl = mean(lower.CL),
               ucl = mean(upper.CL))
  return(pred)
}
elev.pred.males <- elev.pred.fun(machos, c.hat.adults.nb)
elev.pred.females <- elev.pred.fun(hembras, c.hat.adults.nb)
elev.pred.juveniles <- elev.pred.fun(juvs, c.hat.juvs.neg)

# 2. SLOPE
slope.sim <- seq(min(covs$slope), max(covs$slope), length.out = 30)
slope.new <- (slope.sim - mean(covs$slope))/sd(covs$slope)
## predict function for slope effect
slope.pred.fun <- function(mod.list, group.chat){
  pred = as.data.frame(modavgPred(cand.set = mod.list, type = "response", 
                                   parm.type = "lambda",
                                   newdata = 
                                     data.frame(elev = 0, 
                                                slope = rep(slope.new, 8),
                                                aspect = c(rep("N", 60), 
                                                           rep("E", 60), 
                                                           rep("S", 60), 
                                                           rep("W", 60)),
                                                veg = c(rep(c(rep("Shrubs",30),
                                                              rep("Herbaceous",30)), 
                                                            4))), 
                                   c.hat = group.chat)$matrix.output)
  pred$slope <- rep(slope.sim, 8)
  pred = ddply(pred, .(slope), summarize, 
                density.pred = mean(mod.avg.pred), 
                se = mean(uncond.se), 
                lcl = mean(lower.CL), 
                ucl = mean(upper.CL))
  return(pred)
}
slope.pred.males <- slope.pred.fun(machos, c.hat.adults.nb)
slope.pred.females <- slope.pred.fun(hembras, c.hat.adults.nb)
slope.pred.juveniles <- slope.pred.fun(juvs, c.hat.juvs.neg)

# 3. ASPECT
aspect.pred.fun <- function(mod.list, group.chat){
  pred = as.data.frame(modavgPred(cand.set = mod.list, type = "response", 
                                  parm.type = "lambda",
                                  newdata = 
                                    data.frame(elev = 0, 
                                               slope = 0, 
                                               aspect = c(rep("N", 2), 
                                                          rep("E", 2), 
                                                          rep("S", 2), 
                                                          rep("W", 2)), 
                                               veg = c(rep(c("Shrubs",
                                                             "Herbaceous"), 4))), 
                                  c.hat = group.chat)$matrix.output)
  pred$aspect <- c(rep("N", 2), rep("E", 2), rep("S", 2), rep("W", 2))
  pred = ddply(pred, .(aspect), summarize, 
                density.pred = mean(mod.avg.pred), 
                se = mean(uncond.se), 
                lcl = mean(lower.CL), 
                ucl = mean(upper.CL))
  return(pred)
}
aspect.pred.males <- aspect.pred.fun(machos, c.hat.adults.nb)
aspect.pred.females <- aspect.pred.fun(hembras, c.hat.adults.nb)
aspect.pred.juveniles <- aspect.pred.fun(juvs, c.hat.juvs.neg)

# 4. VEGETATION
veg.pred.fun <- function(mod.list, group.chat){
  pred = as.data.frame(modavgPred(cand.set = mod.list, type = "response", 
                                  parm.type = "lambda",
                                  newdata = 
                                    data.frame(elev = 0, 
                                               slope = 0, 
                                               aspect = c(rep(c("N","E",
                                                                "S","W"),2)), 
                                               veg = c(rep("Shrubs",4),
                                                       rep("Herbaceous",4))), 
                                  c.hat = group.chat)$matrix.output)
  pred$veg = c(rep("Shrubs",4),rep("Herbaceous",4))
  pred = ddply(pred, .(veg), summarize, 
               density.pred = mean(mod.avg.pred), 
               se = mean(uncond.se), 
               lcl = mean(lower.CL), 
               ucl = mean(upper.CL))
  return(pred)
}
veg.pred.males <- veg.pred.fun(machos, c.hat.adults.nb)
veg.pred.females <- veg.pred.fun(hembras, c.hat.adults.nb)
veg.pred.juveniles <- veg.pred.fun(juvs, c.hat.juvs.neg)
  
# combine model-averaged covariate predictions by sex
elev.pred <- rbind(elev.pred.males, elev.pred.females, elev.pred.juveniles)
elev.pred$Sex <- c(rep("Males", 30), rep("Females", 30), rep("Juveniles", 30))
elev.pred$Sex <- factor(elev.pred$Sex, 
                        levels = c("Juveniles", "Females", "Males"))

slope.pred <- rbind(slope.pred.males, slope.pred.females, slope.pred.juveniles)
slope.pred$Sex <- c(rep("Males", 30), rep("Females", 30), rep("Juveniles", 30))
slope.pred$Sex <- factor(slope.pred$Sex, 
                         levels = c("Juveniles", "Females", "Males"))

aspect.pred <- rbind(aspect.pred.males, aspect.pred.females, aspect.pred.juveniles)
aspect.pred$Sex <- c(rep("Males", 4), rep("Females", 4), rep("Juveniles", 4))
aspect.pred$Sex <- factor(aspect.pred$Sex, 
                          levels = c("Juveniles", "Females", "Males"))

veg.pred <- rbind(veg.pred.males, veg.pred.females, veg.pred.juveniles)
veg.pred$Sex <- c(rep("Males", 2), rep("Females", 2), rep("Juveniles", 2))
veg.pred$Sex <- factor(veg.pred$Sex, 
                       levels = c("Juveniles", "Females", "Males"))

# PLOTS
elev.plot <- ggplot(elev.pred, aes(x = elev, y = density.pred, col = Sex)) + 
  geom_line(lwd = 1.1) + geom_line(aes(y = lcl), lty = "dashed") + 
  geom_line(aes(y = ucl), lty = "dashed") + 
  labs(x = "Elevation (m)", y = NULL) + ylim(c(0,7)) + 
  theme_classic() + mythemes + 
  scale_color_brewer(palette = "Dark2")

slope.plot <- ggplot(slope.pred, aes(x = slope, y = density.pred, col = Sex)) + 
  geom_line(lwd = 1.1) + geom_line(aes(y = lcl), lty = "dashed") + 
  geom_line(aes(y = ucl), lty = "dashed") + 
  labs(x = "Slope", y = NULL) + ylim(c(0,7)) + 
  theme_classic() + mythemes + 
  scale_color_brewer(palette = "Dark2")

aspect.plot <- ggplot(aspect.pred, aes(x = aspect, y = density.pred, col = Sex)) +
  geom_point(position=position_dodge(0.5)) + 
  geom_errorbar(aes(ymin = lcl, ymax = ucl), width = 0.5, 
                position=position_dodge(0.5)) + 
  labs(x = "Aspect", y = NULL) + ylim(c(0,7)) + 
  theme_classic() + mythemes + 
  scale_color_brewer(palette = "Dark2")

veg.plot <- ggplot(veg.pred, aes(x = veg, y = density.pred, col = Sex)) + 
  geom_point(position=position_dodge(0.5)) + 
  geom_errorbar(aes(ymin = lcl, ymax = ucl), width = 0.25, 
                position=position_dodge(0.5)) + 
  labs(x = "Vegetation", y = NULL) + ylim(c(0,7)) +
  theme_classic() + mythemes + 
  scale_color_brewer(palette = "Dark2")

combined.pred.plots <- ggarrange(elev.plot, slope.plot, 
                                 aspect.plot, veg.plot, nrow = 2, ncol = 2, 
                                 common.legend = TRUE, legend = "bottom",
                                 labels = c("a", "b", "c", "d"),
                                 label.x = c(rep(0.1, 4)))

annotate_figure(combined.pred.plots,
                left = text_grob(expression(Iguanas ~ ha^-1), 
                                 rot = 90, size = 18))

Adult iguanas, particularly males, seem to show a greater affinity for northern and western slopes.

It appears that the elevation effect on juveniles is possibly a statistical artifact of their small sample size. There may be a lower volume of iguanas at low elevations (i.e., near coastal). But we’ll need a larger sample to confirm that effect.

   

Distribution and abundance

---

Let’s now obtain model-averaged abundance estimates and distribution maps for the iguana population on Santa Fe from the full-island survey in 2011.

First we need to load and stack rasters of the covariates.

library(raster)
library(sp)
library(rgdal)
library(rasterVis)
library(viridis)
# load rasters
elev <- raster("data/elev_z_ha_2")
slope <- raster("data/slope_z_ha_2")
aspect <- raster("data/aspect_ha_2")
veg <- raster("data/veg_ha_2")

# stack rasters
santafe.raster <- stack(elev, slope, aspect, veg)
names(santafe.raster) <- c("elev", "slope", "aspect", "veg")
# note: continuous rasters are on z-scale to match the data in the models
# for aspect: N = 1, E = 2, S = 3, W = 4
# for veg: Shrubs = 1, Herbaceous = 2
plot(santafe.raster)

Now we can make our predictions.

# convert covariate rasters to data frame with each row representing one pixel
raster.covs <- as.data.frame(santafe.raster, xy = TRUE)
raster.covs$ID <- rownames(raster.covs)
# reassign categorical covariates to match what was put into the models
raster.covs$veg <- "Herbaceous"
raster.covs$veg[raster.covs$veg_COUNT == 1610] <- "Shrubs"
raster.covs$aspect <- "E"
raster.covs$aspect[raster.covs$aspect_COUNT == 605] <- "N"
raster.covs$aspect[raster.covs$aspect_COUNT == 809] <- "S"
raster.covs$aspect[raster.covs$aspect_COUNT == 279] <- "W"
newdat <- 
  na.omit(data.frame(elev = raster.covs$elev, 
                     slope = raster.covs$slope, 
                     aspect = as.factor(raster.covs$aspect), 
                     veg = as.factor(raster.covs$veg)))

## males
male.pred <- modavgPred(cand.set = machos, type = "response", 
                        parm.type = "lambda", newdata = newdat, 
                        c.hat = c.hat.adults.nb)
male.pred <- data.frame(ID = rownames(newdat),
                        lambda = male.pred$mod.avg.pred,
                        lcl = male.pred$lower.CL,
                        ucl = male.pred$upper.CL)
# combine predictions with XY data
male.pred <- merge(male.pred, raster.covs, by = "ID", all = TRUE)
male.pred.est <- male.pred[,c(5,6,2)]
male.pred.lower <- male.pred[,c(5,6,3)]
male.pred.upper <- male.pred[,c(5,6,4)]

## females
female.pred <- modavgPred(cand.set = hembras, type = "response", 
                          parm.type = "lambda", newdata = newdat, 
                          c.hat = c.hat.adults.nb)
female.pred <- data.frame(ID = rownames(newdat),
                        lambda = female.pred$mod.avg.pred,
                        lcl = female.pred$lower.CL,
                        ucl = female.pred$upper.CL)
# combine predictions with XY data
female.pred <- merge(female.pred, raster.covs, by = "ID", all = TRUE)
female.pred.est <- female.pred[,c(5,6,2)]
female.pred.lower <- female.pred[,c(5,6,3)]
female.pred.upper <- female.pred[,c(5,6,4)]

## juveniles
juv.pred <- modavgPred(cand.set = juvs, type = "response", 
                          parm.type = "lambda", newdata = newdat, 
                       c.hat = c.hat.juvs.neg)
juv.pred <- data.frame(ID = rownames(newdat),
                        lambda = juv.pred$mod.avg.pred,
                        lcl = juv.pred$lower.CL,
                        ucl = juv.pred$upper.CL)
# combine predictions with XY data
juv.pred <- merge(juv.pred, raster.covs, by = "ID", all = TRUE)
juv.pred.est <- juv.pred[,c(5,6,2)]
juv.pred.lower <- juv.pred[,c(5,6,3)]
juv.pred.upper <- juv.pred[,c(5,6,4)]

## total
## from subgroup estimates
total.pred.sum = data.frame(x = juv.pred.est$x,
                            y = juv.pred.est$y,
                            lambda = 
                              juv.pred.est$lambda + 
                              male.pred.est$lambda +
                              female.pred.est$lambda)
total.pred.sum.lower = data.frame(x = juv.pred.lower$x,
                                  y = juv.pred.lower$y,
                                  lcl = 
                                    juv.pred.lower$lcl + 
                                    male.pred.lower$lcl +
                                    female.pred.lower$lcl)
total.pred.sum.upper = data.frame(x = juv.pred.upper$x,
                                  y = juv.pred.upper$y,
                                  ucl = 
                                    juv.pred.upper$ucl + 
                                    male.pred.upper$ucl +
                                    female.pred.upper$ucl)
## from full dataset models
total.pred <- modavgPred(cand.set = all, type = "response", 
                         parm.type = "lambda", newdata = newdat, 
                         c.hat = c.hat.all.nb)
total.pred <- data.frame(ID = rownames(newdat),
                        lambda = total.pred$mod.avg.pred,
                        lcl = total.pred$lower.CL,
                        ucl = total.pred$upper.CL)
# combine predictions with XY data
total.pred <- merge(total.pred, raster.covs, by = "ID", all = TRUE)
total.pred.est <- total.pred[,c(5,6,2)]
total.pred.lower <- total.pred[,c(5,6,3)]
total.pred.upper <- total.pred[,c(5,6,4)]

# combine predictions into one plot
library(lattice)
library(grid)
library(gridExtra)
library(colorRamps)
library(grDevices)

r1 <- ggplot(juv.pred.est, aes(x = x, y = y)) + 
  geom_tile(aes(fill = lambda)) +
  geom_polygon(inherit.aes = FALSE, data = santafe.shp, 
               color = "black", fill = "transparent", lwd = 1.1, 
               aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") +  
  theme_bw() + mythemes +
  labs(x = "\nLongitude", y = "Latitude\n", title = "(a) juveniles") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + coord_equal()

r2 <- ggplot(female.pred.est, aes(x = x, y = y)) + 
  geom_tile(aes(fill = lambda)) + 
  geom_polygon(inherit.aes = FALSE, data = santafe.shp, 
               color = "black", fill = "transparent", lwd = 1.1, 
               aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes +
  labs(x = "\nLongitude", y = "Latitude\n", title = "(b) females") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + coord_equal()

r3 <- ggplot(male.pred.est, aes(x = x, y = y)) + 
  geom_tile(aes(fill = lambda)) + 
  geom_polygon(inherit.aes = FALSE, data = santafe.shp, 
               color = "black", fill = "transparent", lwd = 1.1, 
               aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes + 
  labs(x = "\nLongitude", y = "Latitude\n", title = "(c) males") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + coord_equal()

r4 <- ggplot(total.pred.sum, aes(x = x, y = y)) + 
  geom_tile(aes(fill = lambda)) + 
  geom_polygon(inherit.aes = FALSE, data = santafe.shp, 
               color = "black", fill = "transparent", lwd = 1.1, 
               aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes + 
  labs(x = "\nLongitude", y = "Latitude\n", title = "(d) total") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + coord_equal()

ggarrange(r1, r2, r3, r4, ncol = 2, nrow = 2, common.legend = FALSE)

What is the total estimated population size (with confidence limits) from summing the pixel values of juveniles, females, and males?

juvenile.pop.2011 <- data.frame(abundance = sum(na.omit(juv.pred$lambda)), 
                                lcl = sum(na.omit(juv.pred$lcl)),
                                ucl = sum(na.omit(juv.pred$ucl)))
female.pop.2011 <- data.frame(abundance = sum(na.omit(female.pred$lambda)), 
                                lcl = sum(na.omit(female.pred$lcl)),
                                ucl = sum(na.omit(female.pred$ucl)))
male.pop.2011 <- data.frame(abundance = sum(na.omit(male.pred$lambda)), 
                                lcl = sum(na.omit(male.pred$lcl)),
                                ucl = sum(na.omit(male.pred$ucl)))
# total estimate as sum of separate juvenile and adult estimates
total.pop.2011 <- data.frame(abundance = 
                               juvenile.pop.2011$abundance +
                               female.pop.2011$abundance +
                               male.pop.2011$abundance,
                             lcl = 
                               juvenile.pop.2011$lcl +
                               female.pop.2011$lcl +
                               male.pop.2011$lcl,
                             ucl =
                               juvenile.pop.2011$ucl +
                               female.pop.2011$ucl +
                               male.pop.2011$ucl)

# separate total estimate from the complete dataset
total.pop.2011.sep <- data.frame(abundance = sum(na.omit(total.pred$lambda)), 
                                 lcl = sum(na.omit(total.pred$lcl)),
                                 ucl = sum(na.omit(total.pred$ucl)))

# print the population estimates
iguana.pop.2011 <- rbind(juvenile.pop.2011, female.pop.2011, 
                         male.pop.2011, total.pop.2011)
iguana.pop.2011$type <- c("juveniles", "females", "males", "total")
iguana.pop.2011 <- iguana.pop.2011[,c(4,1,2,3)]
iguana.pop.2011

##        type abundance       lcl       ucl
## 1 juveniles  727.3709  281.4258  2486.768
## 2   females 1794.3660  876.2292  3596.923
## 3     males 2109.0771 1073.7477  4133.852
## 4     total 4630.8140 2231.4027 10217.543

# print the separate total population estimate
total.pop.2011.sep

##   abundance      lcl      ucl
## 1  4109.258 2481.544 6814.215

We can also map the 95% CI bounds for these density estimates.

Here are the lower bounds of the density estimates.

r1 <- ggplot(juv.pred.lower, aes(x = x, y = y)) + 
  geom_tile(aes(fill = lcl)) +
  geom_polygon(inherit.aes = FALSE, 
               data = santafe.shp, color = "black", fill = "transparent", 
               lwd = 1.1, aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") +  
  theme_bw() + mythemes +
  labs(x = "\nLongitude", y = "Latitude\n", title = "(a) juveniles") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + 
  coord_equal()

r2 <- ggplot(female.pred.lower, aes(x = x, y = y)) + 
  geom_tile(aes(fill = lcl)) + 
  geom_polygon(inherit.aes = FALSE, 
               data = santafe.shp, color = "black", fill = "transparent", 
               lwd = 1.1, aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes +
  labs(x = "\nLongitude", y = "Latitude\n", title = "(b) females") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + 
  coord_equal()

r3 <- ggplot(male.pred.lower, aes(x = x, y = y)) + 
  geom_tile(aes(fill = lcl)) + 
  geom_polygon(inherit.aes = FALSE, 
               data = santafe.shp, color = "black", fill = "transparent", 
               lwd = 1.1, aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes + 
  labs(x = "\nLongitude", y = "Latitude\n", title = "(c) males") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + 
  coord_equal()

r4 <- ggplot(total.pred.sum.lower, aes(x = x, y = y)) + 
  geom_tile(aes(fill = lcl)) + 
  geom_polygon(inherit.aes = FALSE, 
               data = santafe.shp, color = "black", fill = "transparent", 
               lwd = 1.1, aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes + 
  labs(x = "\nLongitude", y = "Latitude\n", title = "(d) total") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + 
  coord_equal()

ggarrange(r1, r2, r3, r4, ncol = 2, nrow = 2, common.legend = FALSE)

And here are the upper bounds.

r1 <- ggplot(juv.pred.upper, aes(x = x, y = y)) + 
  geom_tile(aes(fill = ucl)) + 
  geom_polygon(inherit.aes = FALSE, 
               data = santafe.shp, color = "black", fill = "transparent", 
               lwd = 1.1, aes(x = long, y = lat)) +
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") +  
  theme_bw() + mythemes +
  labs(x = "\nLongitude", y = "Latitude\n", title = "(a) juveniles") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + 
  coord_equal()

r2 <- ggplot(female.pred.upper, aes(x = x, y = y)) + 
  geom_tile(aes(fill = ucl)) + 
  geom_polygon(inherit.aes = FALSE, 
               data = santafe.shp, color = "black", fill = "transparent", 
               lwd = 1.1, aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes + 
  labs(x = "\nLongitude", y = "Latitude\n", title = "(b) females") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + 
  coord_equal()

r3 <- ggplot(male.pred.upper, aes(x = x, y = y)) + 
  geom_tile(aes(fill = ucl)) + 
  geom_polygon(inherit.aes = FALSE, 
               data = santafe.shp, color = "black", fill = "transparent", 
               lwd = 1.1, aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes +
  labs(x = "\nLongitude", y = "Latitude\n", title = "(c) males") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + 
  coord_equal()

r4 <- ggplot(total.pred.sum.upper, aes(x = x, y = y)) + 
  geom_tile(aes(fill = ucl)) + 
  geom_polygon(inherit.aes = FALSE, 
               data = santafe.shp, color = "black", fill = "transparent", 
               lwd = 1.1, aes(x = long, y = lat)) + 
  scale_fill_gradientn(colors = c("darkgreen", "yellow", "red3"), 
                       na.value = "transparent") + 
  theme_bw() + mythemes + 
  labs(x = "\nLongitude", y = "Latitude\n", title = "(d) total") + 
  guides(fill = guide_colorbar(raster = TRUE, 
                               title = expression(Iguanas ~ ha^-1), 
                               title.position = "top")) + 
  coord_equal()

ggarrange(r1, r2, r3, r4, ncol = 2, nrow = 2, common.legend = FALSE)

Changes from 2011–2020

Now let’s use hierarchical distance sampling models to compare density estimates between years from our iguana transects. We are only using a subset of the original island-wide transects here that are within the center of the island where tortoises were released. These transects (n=28), and the permanent plots in between them, were visited three times, once before and twice after tortoise introduction.

Here is all our data prep code to run the distance sampling models in unmarked. We’re going to stack transects by year to get abundance estimates as a function of time, tortoise density, and other covariates.

# detach plyr to avoid conflicts
detach("package:plyr", unload = TRUE)
### LOAD DISTANCE SAMPLING DATA OF SUBSET OF TRANSECTS ###
library(readxl)
iguanas <- suppressMessages(read_excel("data/iguanas_distsamp_2011_2017_2020.xlsx", 
                                       na = "NA"))
iguanas$transect_yr <- as.factor(paste(iguanas$transect, iguanas$year, sep = "-"))

# make time a continuous covariate and impute mean survey time for missing transects
iguanas$hm <- hour(iguanas$time) + minute(iguanas$time)/60
iguanas$hm[is.na(iguanas$hm)] <- mean(iguanas$hm, na.rm = T)

# get mean times for each transect_yr
transect.times <- iguanas %>%
  group_by(transect_yr) %>%
  summarise(time = mean(hm)) %>%
  ungroup()

# number of visits for each transect
transect.visits <- iguanas %>%
  distinct(transect, year) %>%
  group_by(transect) %>%
  summarise(visits = n()) %>%
  ungroup()

# load transect buffers
iguana.buffs <- readOGR("data/iguana_transects_50m_buff.shp", verbose=FALSE)
iguana.buffs <- spTransform(iguana.buffs, CRS("+init=epsg:32715"))

# get zonal statistics for tortoise densities in iguana transect buffers
buff.2017 <- 
  data.frame(transect = iguana.buffs$transect,
             tden = c(raster::extract(tortoise.brick.adj$Y2017, 
                                      iguana.buffs, fun = mean, na.rm = TRUE)),
             tden2yr = c(raster::extract(mean(tortoise.brick.adj[[1:2]]), 
                                         iguana.buffs, fun = mean, na.rm = TRUE)),
             tden5yr = c(raster::extract(mean(tortoise.brick.adj[[1:2]], 
                                              tortoise.brick.adj[[1:3]]*0), 
                                         iguana.buffs, fun = mean, na.rm = TRUE)),
             year = 2017)
buff.2020 <- 
  data.frame(transect = iguana.buffs$transect,
             tden = c(raster::extract(tortoise.brick.adj$Y2020, 
                                      iguana.buffs, fun = mean, na.rm = TRUE)),
             tden2yr = c(raster::extract(mean(tortoise.brick.adj[[4:5]]), 
                                         iguana.buffs, fun = mean, na.rm = TRUE)),
             tden5yr = c(raster::extract(mean(tortoise.brick.adj[[1:5]]),
                                         iguana.buffs, fun = mean, na.rm = TRUE)), 
             year = 2020)

buff.tden <- rbind(buff.2017, buff.2020)

# subset transects to those surveyed in all three years
iguanas.sub <- iguanas %>%
  filter(transect %in% transect.visits$transect[transect.visits$visits == 3]) %>%
  droplevels() %>%
  as.data.frame()

# summarize total counts of iguanas each year within same subset of transects
iguanas.sub %>%
  filter(!is.na(distance)) %>%
  group_by(year) %>%
  summarise(n_iguanas = n()) %>%
  ungroup()

## # A tibble: 3 x 2
##    year n_iguanas
##   <dbl>     <int>
## 1  2011        35
## 2  2017        59
## 3  2020        73

# identify distance to truncate iguana observations (convert to NAs)
iguanas.sub$quantile <- q.rank(iguanas.sub$distance)
max.dist <- min(iguanas.sub$distance[iguanas.sub$quantile >= 0.975], na.rm = T)

# prepare observations and covariates for unmarked
ydat <- formatDistData(iguanas.sub,
                       distCol="distance",
                       transectNameCol="transect_yr",
                       dist.breaks=seq(0,max.dist,length.out = 6))

### LOAD COVARIATES ###
covs <- read.csv(file = "data/distsamp_covars.csv", 
                 header = TRUE, row.names="transect") 

# subset to transects surveyed in all three years
covs <- covs %>%
  mutate(transect = rownames(.)) %>%
  filter(transect %in% transect.visits$transect[transect.visits$visits == 3]) %>%
  as.data.frame()

# standardize continuous covariates
covs$elev.z <- scale(covs$elev)
covs$slope.z <- scale(covs$slope)

# repeat data frame for each survey year
covs <- rbind(covs, covs, covs)
covs$year <- c(rep(2011, length(unique(covs$transect))), 
               rep(2017, length(unique(covs$transect))), 
               rep(2020, length(unique(covs$transect))))

# add tortoise density and time covariates
covs <- covs %>%
  left_join(buff.tden, by = c("transect", "year")) %>%
  mutate_all(~replace(., is.na(.), 0)) %>%
  mutate(transect_yr = paste(transect, year, sep = "-")) %>%
  filter(transect_yr %in% iguanas$transect_yr) %>%
  left_join(transect.times, by = c("transect_yr")) %>%
  mutate(tden.z = scale(tden),
         tden2yr.z = scale(tden2yr),
         tden5yr.z = scale(tden5yr),
         time.z = scale(time)) %>%
  droplevels() %>%
  as.data.frame() 

ydat.df <- data.frame(ydat) %>%
  mutate(transect_yr = rownames(.)) %>%
  left_join(covs, by = "transect_yr")

umf <- 
  unmarkedFrameDS(y = ydat, 
                  siteCovs = data.frame(time = ydat.df$time.z,
                                        year = as.factor(ydat.df$year),
                                        elev = ydat.df$elev.z,
                                        slope = ydat.df$slope.z,
                                        aspect = ydat.df$aspect,
                                        veg = ydat.df$veg,
                                        tden = ydat.df$tden.z,
                                        tden2yr = ydat.df$tden2yr.z,
                                        tden5yr = ydat.df$tden5yr.z), 
                  dist.breaks=seq(0,max.dist,length.out = 6),
                  unitsIn="m", survey="line", tlength = rep(500, nrow(covs)))

summary(umf)

## unmarkedFrameDS Object
## 
## line-transect survey design
## Distance class cutpoints (m):  0 3 6 9 12 15 
## 
## 84 sites
## Maximum number of distance classes per site: 5 
## Mean number of distance classes per site: 5 
## Sites with at least one detection: 68 
## 
## Tabulation of y observations:
##   0   1   2   3   4   5 
## 306  82  20   8   1   3 
## 
## Site-level covariates:
##       time           year         elev             slope         aspect
##  Min.   :-1.7269   2011:28   Min.   :-1.3893   Min.   :-1.9942   E: 6  
##  1st Qu.:-0.6963   2017:28   1st Qu.:-0.7509   1st Qu.:-0.5595   N:36  
##  Median :-0.1864   2020:28   Median :-0.1790   Median :-0.1439   S:33  
##  Mean   : 0.0000             Mean   : 0.0000   Mean   : 0.0000   W: 9  
##  3rd Qu.: 0.4582             3rd Qu.: 0.7461   3rd Qu.: 0.6308         
##  Max.   : 2.2739             Max.   : 2.3659   Max.   : 2.0069         
##          veg          tden            tden2yr           tden5yr       
##  Herbaceous:81   Min.   :-0.3951   Min.   :-0.3652   Min.   :-0.3005  
##  Shrubs    : 3   1st Qu.:-0.3951   1st Qu.:-0.3652   1st Qu.:-0.3005  
##                  Median :-0.3725   Median :-0.3649   Median :-0.3003  
##                  Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
##                  3rd Qu.:-0.1687   3rd Qu.:-0.2565   3rd Qu.:-0.2075  
##                  Max.   : 5.0267   Max.   : 5.4047   Max.   : 5.9990

Let’s examine our covariates to see if we have any colinearity in our geographic and new tortoise covariates before running our distance sampling models.

## 
## 
## Variance inflation factors
## 
##             GVIF Df GVIF^(1/2Df)
## aspect  1.705008  3     1.093002
## veg     1.154379  1     1.074420
## elev.z  1.193217  1     1.092345
## slope.z 1.422623  1     1.192738
## year    1.115498  1     1.056171
## tden.z  1.296344  1     1.138571

## 
## 
## Variance inflation factors
## 
##               GVIF Df GVIF^(1/2Df)
## aspect    1.672575  3     1.089509
## veg       1.160633  1     1.077327
## elev.z    1.179107  1     1.085867
## slope.z   1.414742  1     1.189429
## year      1.098115  1     1.047910
## tden5yr.z 1.230408  1     1.109238

The VIF scores indicate that there is no colinearity among our covariates.

Now I’ll create our models. First we want to identify the correct detection function.

# create six base models and compare the global model for three different detection functions 
haz.t <- distsamp(
  ~time+year ~elev+slope+veg+tden5yr+year,
  umf, keyfun="hazard", output="density", unitsOut="ha")

haz.t2 <- distsamp(
  ~time+I(time^2)+year ~elev+slope+veg+tden5yr+year,
  umf, keyfun="hazard", output="density", unitsOut="ha")

hn.t <- distsamp(
  ~time+year ~elev+slope+veg+tden5yr+year,
  umf, keyfun="halfnorm", output="density", unitsOut="ha")

hn.t2 <- distsamp(
  ~time+I(time^2)+year ~elev+slope+veg+tden5yr+year,
  umf, keyfun="halfnorm", output="density", unitsOut="ha")

nexp.t <- distsamp(
  ~time+year ~elev+slope+veg+tden5yr+year,
  umf, keyfun="exp", output="density", unitsOut="ha")

nexp.t2 <- distsamp(
  ~time+I(time^2)+year ~elev+slope+veg+tden5yr+year,
  umf, keyfun="exp", output="density", unitsOut="ha")

aictab(cand.set = list(haz.t, hn.t, nexp.t,
                       haz.t2, hn.t2, nexp.t2),
       modnames = c("hazard", "halfnorm", "negexp",
                    "hazard2", "halfnorm2", "negexp2"))

## 
## Model selection based on AICc:
## 
##            K   AICc Delta_AICc AICcWt Cum.Wt      LL
## negexp    11 580.36       0.00   0.55   0.55 -277.35
## negexp2   12 581.59       1.24   0.30   0.85 -276.60
## hazard    12 583.84       3.48   0.10   0.95 -277.72
## hazard2   13 585.19       4.83   0.05   1.00 -276.99
## halfnorm2 12 592.00      11.64   0.00   1.00 -281.80
## halfnorm  11 592.28      11.92   0.00   1.00 -283.31

We’re going to go with the negative exponential detection function to model iguana density. Let’s run our goodness of fit tests.

set.seed(1)
GoF <- parboot(nexp.t, fitstats, nsim=1000, report=5) ; GoF

## t0 = 185.6701 502.293 103.606

## 
## Call: parboot(object = nexp.t, statistic = fitstats, nsim = 1000, report = 5)
## 
## Parametric Bootstrap Statistics:
##               t0 mean(t0 - t_B) StdDev(t0 - t_B) Pr(t_B > t0)
## SSE          186          27.19            20.19       0.0979
## Chisq        502         101.62            69.73       0.0519
## freemanTukey 104           3.79             7.17       0.2977
## 
## t_B quantiles:
##               0% 2.5% 25% 50% 75% 97.5% 100%
## SSE          105  124 144 157 172   200  236
## Chisq        254  307 360 390 428   559 1087
## freemanTukey  79   85  95 100 105   114  120
## 
## t0 = Original statistic computed from data
## t_B = Vector of bootstrap samples

observed <- data.frame(test = names(GoF@t0),
                       value = GoF@t0) %>% melt(id = "test")
GoF@t.star %>%
  melt() %>%
  dplyr::rename(test = Var2) %>%
  ggplot(aes(x = value)) +
  geom_histogram(col = "white", fill = "grey5", alpha = 0.3) +
  geom_vline(data = observed, aes(xintercept = value), 
             col = "blue", lwd = 0.9) +
  facet_wrap(~test, nrow = 3, scales = "free") + 
  theme_classic() + mythemes +
  labs(x = "Bootstrapped statistic", y = "Frequency")

c.hat <- GoF@t0[2] / mean(GoF@t.star[,2]); c.hat

##    Chisq 
## 1.253623

The global model seems to fit pretty well.

There is very slight overdispersion, so let’s account for that in our model rankings and estimates.

Here is our candidate list of models.

# create candidate models, rank with QAIC
nexp.null <- distsamp(
  ~1 ~1,
  umf, keyfun="exp", output="density", unitsOut="ha")

nexp.year <- distsamp(
  ~time+year ~year,
  umf, keyfun="exp", output="density", unitsOut="ha")

nexp.hab <- distsamp(
  ~time+year ~elev+slope+veg+year,
  umf, keyfun="exp", output="density", unitsOut="ha")

nexp.tden <- distsamp(
  ~time+year ~tden+year,
  umf, keyfun="exp", output="density", unitsOut="ha")

nexp.tden5y <- distsamp(
  ~time+year ~tden5yr+year,
  umf, keyfun="exp", output="density", unitsOut="ha")

nexp.full <- distsamp(
  ~time+year ~elev+slope+veg+tden+year,
  umf, keyfun="exp", output="density", unitsOut="ha")

nexp.full.5y <- distsamp(
  ~time+year ~elev+slope+veg+tden5yr+year,
  umf, keyfun="exp", output="density", unitsOut="ha")

We’ll rank models with the aictab function from the AICcmodavg package.

iguana.rankings <- 
  aictab(cand.set = list(nexp.null, nexp.year, nexp.hab, nexp.tden, 
                         nexp.tden5y, nexp.full, nexp.full.5y), c.hat = c.hat,
         modnames = c("null", "year", "habitat", "tortoises", 
                      "tortoises (5 yr)", "habitat + tortoises", 
                      "habitat + tortoises (5 yr)"))
iguana.rankings

## 
## Model selection based on QAICc:
## (c-hat estimate = 1.253623)
## 
##                             K  QAICc Delta_QAICc QAICcWt Cum.Wt Quasi.LL
## year                        8 462.01        0.00    0.47   0.47  -222.05
## tortoises (5 yr)            9 463.45        1.44    0.23   0.71  -221.51
## tortoises                   9 464.16        2.15    0.16   0.87  -221.86
## null                        3 464.97        2.96    0.11   0.98  -229.34
## habitat                    11 469.07        7.05    0.01   0.99  -221.70
## habitat + tortoises (5 yr) 12 470.86        8.85    0.01   1.00  -221.24
## habitat + tortoises        12 471.57        9.56    0.00   1.00  -221.59

write.csv(iguana.rankings, "data/iguana_model_rankings_stacked.csv")

Interesting. The year model is on top and nothing is within 2 QAICc units, which suggests that iguana population does not vary with our tortoise and/or environmental covariates.

Let’s look at the parameter estimates from that year model.

summary(nexp.year)

## 
## Call:
## distsamp(formula = ~time + year ~ year, data = umf, keyfun = "exp", 
##     output = "density", unitsOut = "ha")
## 
## Density (log-scale):
##             Estimate    SE     z  P(>|z|)
## (Intercept)    1.509 0.256 5.902 3.60e-09
## year2017       0.310 0.323 0.959 3.38e-01
## year2020       0.294 0.315 0.935 3.50e-01
## 
## Detection (log-scale):
##                 Estimate     SE     z  P(>|z|)
## rate(Intercept)   0.9984 0.1943 5.138 2.77e-07
## ratetime          0.0314 0.0654 0.480 6.32e-01
## rateyear2017      0.2372 0.2515 0.943 3.46e-01
## rateyear2020      0.4772 0.2505 1.905 5.68e-02
## 
## AIC: 570.7231 
## Number of sites: 84
## optim convergence code: 0
## optim iterations: 164 
## Bootstrap iterations: 0 
## 
## Survey design: line-transect
## Detection function: exp
## UnitsIn: m
## UnitsOut: ha

It does not appear that iguana density changes significantly over time. Detection rates may be greater in 2020. No hour effect on detection probability.

Out of curiosity, what do the next two models with the tortoise density look like?

nexp.tden5y

## 
## Call:
## distsamp(formula = ~time + year ~ tden5yr + year, data = umf, 
##     keyfun = "exp", output = "density", unitsOut = "ha")
## 
## Density:
##             Estimate     SE     z  P(>|z|)
## (Intercept)   1.4805 0.2571  5.76 8.52e-09
## tden5yr      -0.0959 0.0879 -1.09 2.76e-01
## year2017      0.3236 0.3232  1.00 3.17e-01
## year2020      0.3571 0.3186  1.12 2.62e-01
## 
## Detection:
##                 Estimate     SE     z  P(>|z|)
## rate(Intercept)   1.0017 0.1945 5.152 2.58e-07
## ratetime          0.0469 0.0672 0.698 4.85e-01
## rateyear2017      0.2300 0.2515 0.914 3.61e-01
## rateyear2020      0.4743 0.2505 1.893 5.83e-02
## 
## AIC: 571.3748

nexp.tden

## 
## Call:
## distsamp(formula = ~time + year ~ tden + year, data = umf, keyfun = "exp", 
##     output = "density", unitsOut = "ha")
## 
## Density:
##             Estimate     SE     z  P(>|z|)
## (Intercept)   1.4878 0.2578  5.77 7.86e-09
## tden         -0.0543 0.0822 -0.66 5.09e-01
## year2017      0.3333 0.3247  1.03 3.05e-01
## year2020      0.3316 0.3192  1.04 2.99e-01
## 
## Detection:
##                 Estimate    SE     z  P(>|z|)
## rate(Intercept)   1.0002 0.194 5.146 2.67e-07
## ratetime          0.0405 0.067 0.604 5.46e-01
## rateyear2017      0.2332 0.252 0.927 3.54e-01
## rateyear2020      0.4756 0.250 1.898 5.76e-02
## 
## AIC: 572.2632

Tortoise density has no effect on iguana density.

Let’s use the top model plot out our iguana density estimates for 2011, 2017, and 2020 (and include our tortoise density estimates in the plot as a reference).

library(adehabitatHR)
# get minimal convex polygon of transect coordinates
transect.points <- 
  SpatialPoints(sp::coordinates(subset(iguana.buffs, 
                                       transect %in% iguanas.sub$transect)))

survey.zone <- mcp(transect.points, percent = 100)
writeOGR(obj = survey.zone, dsn = getwd(),  layer = "data/core_survey_zone", 
         driver="ESRI Shapefile", overwrite_layer=TRUE)

# get iguana density predictions from top model
i.lambda <- predict(nexp.year, type = "state", c.hat = c.hat, 
                      newdata = data.frame(year = c("2011", "2017", "2020")))

i.lambda$N_hat = i.lambda$Predicted * survey.zone$area
i.lambda$N_lower = i.lambda$lower * survey.zone$area
i.lambda$N_upper = i.lambda$upper * survey.zone$area
i.lambda$pct_change = (i.lambda$N_hat - i.lambda$N_hat[1])/i.lambda$N_hat[1]
i.lambda$pct_change_lwr = (i.lambda$N_lower - i.lambda$N_lower[1])/i.lambda$N_lower[1]
i.lambda$pct_change_upr = (i.lambda$N_upper - i.lambda$N_upper[1])/i.lambda$N_upper[1] 

i.lambda

##   Predicted       SE    lower    upper    N_hat   N_lower  N_upper pct_change
## 1  4.523015 1.156634 2.740043 7.466186 1539.035  932.3476 2540.501  0.0000000
## 2  6.164160 1.215416 4.188307 9.072130 2097.464 1425.1450 3086.952  0.3628430
## 3  6.069661 1.112135 4.238381 8.692184 2065.309 1442.1836 2957.668  0.3419501
##   pct_change_lwr pct_change_upr
## 1      0.0000000      0.0000000
## 2      0.5285555      0.2150956
## 3      0.5468304      0.1642066

# get mean tortoise density in 2017 and 2020 in survey zone
t.lambda <- 
  data.frame(estimate = c(0, raster::extract(tortoise.brick.adj$Y2017, 
                                             survey.zone, 
                                             fun = mean, na.rm = TRUE),
                          raster::extract(tortoise.brick.adj$Y2020, 
                                          survey.zone, 
                                          fun = mean, na.rm = TRUE)),
             lower = c(0, raster::extract(tortoise.brick.adj.lcl$Y2017, 
                                          survey.zone, 
                                          fun = mean, na.rm = TRUE),
                       raster::extract(tortoise.brick.adj.lcl$Y2020, 
                                       survey.zone, 
                                       fun = mean, na.rm = TRUE)),
             upper = c(0, raster::extract(tortoise.brick.adj.ucl$Y2017, 
                                          survey.zone, 
                                          fun = mean, na.rm = TRUE),
                               raster::extract(tortoise.brick.adj.ucl$Y2020, 
                                               survey.zone,
                                       fun = mean, na.rm = TRUE)))

# combine iguana and tortoise density data frames for plotting together
sf.densities <- data.frame(density = c(i.lambda$Predicted, t.lambda$estimate),
                           lcl = c(i.lambda$lower, t.lambda$lower),
                           ucl = c(i.lambda$upper, t.lambda$upper),
                           Year = c(rep(c("2011", "2017", "2020"),2)),
                           species = c(rep("iguana", 3), rep("tortoise", 3)))

# print density / abundance table
sf.densities

##    density      lcl      ucl Year  species
## 1 4.523015 2.740043 7.466186 2011   iguana
## 2 6.164160 4.188307 9.072130 2017   iguana
## 3 6.069661 4.238381 8.692184 2020   iguana
## 4 0.000000 0.000000 0.000000 2011 tortoise
## 5 1.046474 0.976587 1.135559 2017 tortoise
## 6 1.294435 1.148891 1.474581 2020 tortoise

# plot
distsamp.plot <-
  ggplot(sf.densities, aes(Year, density, color = species)) + 
  geom_pointrange(aes(ymin = lcl, ymax = ucl)) +
  geom_vline(aes(xintercept = 1.71), col = "grey50", 
             lty = "dashed", lwd = 1.1) +
  geom_hline(aes(yintercept = 0), lty = "dashed") +
  geom_pointrange(aes(ymin = lcl, ymax = ucl)) +
  theme_classic() + mythemes + 
  labs(x = "Year", y = "Density (per ha)") + ylim(0,10) +
  annotate("text", x = 3.2, y = sf.densities$density[3], 
           label = "iguanas", col = col2[1], size = 4) +
  annotate("text", x = 3.2, y = sf.densities$density[6], 
           label = "tortoises", col = col2[2], size = 4) +
  scale_color_manual(values = col2) + theme(legend.position = "none")

distsamp.plot

The population may increased slightly from 2011 to 2020 (~ 529 [421–512] individuals or 34% [17–55%]), but there is a lot of uncertainty around those estimates so there is no strong evidence to support any iguana change over time or tortoise impact on iguana distribution or abundance. This could change as tortoises get larger and begin reproducing, thus having a more sustained impact on the environment in Santa Fe. Future monitoring will be essential to verify any impacts on the iguana population.

Let’s ask the same question about iguana population change using the repeated plot counts from 2011 and 2020.

Plot data

# load data
plots2011 <- 
  suppressMessages(read_excel("data/iguana_plots_2011_2017_2020.xlsx", 
                              na = "NA", sheet = "2011")) %>% arrange(Punto)
plots2017 <- 
  suppressMessages(read_excel("data/iguana_plots_2011_2017_2020.xlsx", 
                              na = "NA", sheet = "2017")) %>% arrange(Punto)
plots2020 <- 
  suppressMessages(read_excel("data/iguana_plots_2011_2017_2020.xlsx", 
                              na = "NA", sheet = "2020")) %>% arrange(Punto)

Plots were also measured in 2017, but iguana data from at least 10 plots from the core zone were lost and unrecoverable. So we will focus on the two years, 2011 (before) and 2020 (after) which we have complete data for.

# filter the 2011 data to include only those plots that were surveyed in 2020
plots2011 <- plots2011 %>%
  filter(Punto %in% plots2020$Punto)

# combine the 2011 and 2020 data
iguana_plots <- 
  data.frame(Plot = plots2011$Punto, 
             Lat = plots2011$Latitud, Lon = plots2011$Longitud,
             ITM2011 = plots2011$ITM, ITH2011 = plots2011$ITH, 
             ITJ2011 = plots2011$ITJ, ITT2011 = plots2011$ITT, 
             ITM2020 = plots2020$ITM, ITH2020 = plots2020$ITH, 
             ITJ2020 = plots2020$ITJ, ITT2020 = plots2020$ITT,
             TG2011 = 0, TG2020 = plots2020$TGH+plots2020$TGM+plots2020$TGJ,
             HI2011 = plots2011$HI, HI2020 = plots2020$HI,
             CA2011 = plots2011$CA, CS2011 = plots2011$CS, 
             CJ2011 = plots2011$CJ, CT2011 = plots2011$CT,
             CA2020 = plots2020$CA, CS2020 = plots2020$CS, 
             CJ2020 = plots2020$CJ, CT2020 = plots2020$CT)

Wilcoxin tests

First let’s use a Wilcoxin test to compare iguana and iguana fecal density in plots between 2011 and 2020.

# male iguanas
pop.diff.m <- wilcox.test(iguana_plots$ITM2011, iguana_plots$ITM2020, 
                          paired = TRUE); pop.diff.m

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  iguana_plots$ITM2011 and iguana_plots$ITM2020
## V = 49, p-value = 0.8217
## alternative hypothesis: true location shift is not equal to 0

# female iguanas
pop.diff.f <- wilcox.test(iguana_plots$ITH2011, iguana_plots$ITH2020, 
                          paired = TRUE); pop.diff.f

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  iguana_plots$ITH2011 and iguana_plots$ITH2020
## V = 16, p-value = 0.8211
## alternative hypothesis: true location shift is not equal to 0

# total iguanas
pop.diff.t <- wilcox.test(iguana_plots$ITT2011, iguana_plots$ITT2020, 
                          paired = TRUE); pop.diff.t

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  iguana_plots$ITT2011 and iguana_plots$ITT2020
## V = 131, p-value = 0.3243
## alternative hypothesis: true location shift is not equal to 0

# fecal denstiy
fec.diff <- wilcox.test(iguana_plots$HI2011, iguana_plots$HI2020, 
                        paired = TRUE); fec.diff

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  iguana_plots$HI2011 and iguana_plots$HI2020
## V = 20, p-value = 4.513e-08
## alternative hypothesis: true location shift is not equal to 0

According to these tests, there are no differences in iguana density before and after tortoise introductions. But there are a lot of plots with no differences between years, and those measurements are ignored in the significance test. There is a difference in iguana feces (more in 2020), but that may simply be due to human measurement error (including confusion with juvenile tortoise feces).

Let’s also look at the same comparisons with Wilcoxin tests for cactus plot counts.

# juvenile cactus
pop.diff.cj <- wilcox.test(iguana_plots$CJ2011, iguana_plots$CJ2020, 
                           paired = TRUE); pop.diff.cj

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  iguana_plots$CJ2011 and iguana_plots$CJ2020
## V = 21.5, p-value = 3.923e-07
## alternative hypothesis: true location shift is not equal to 0

# subadult cactus
pop.diff.cs <- wilcox.test(iguana_plots$CS2011, iguana_plots$CS2020, 
                           paired = TRUE); pop.diff.cs

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  iguana_plots$CS2011 and iguana_plots$CS2020
## V = 68, p-value = 1.832e-05
## alternative hypothesis: true location shift is not equal to 0

# adult cactus
pop.diff.ca <- wilcox.test(iguana_plots$CA2011, iguana_plots$CA2020, 
                           paired = TRUE); pop.diff.ca

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  iguana_plots$CA2011 and iguana_plots$CA2020
## V = 492.5, p-value = 0.03346
## alternative hypothesis: true location shift is not equal to 0

# total cactus
pop.diff.ct <- wilcox.test(iguana_plots$CT2011, iguana_plots$CT2020, 
                           paired = TRUE); pop.diff.ct

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  iguana_plots$CT2011 and iguana_plots$CT2020
## V = 184, p-value = 0.0008327
## alternative hypothesis: true location shift is not equal to 0

library(broom)
library(tidyr)
iguana_plots %>%
  dplyr::select(Plot, CJ2011, CJ2020, CS2011, CS2020, 
                CA2011, CA2020, CT2011, CT2020) %>%
  pivot_longer(-Plot, names_to = "CountStage", values_to = "Count") %>%
  mutate(Year = ifelse(CountStage %in% c("CJ2011", "CS2011", "CA2011", "CT2011"), 
                       "2011", "2020"),
         Stage = case_when(CountStage %in% c("CJ2011", "CJ2020") ~ "Juvenile",
                           CountStage %in% c("CS2011", "CS2020") ~ "Subadult",
                           CountStage %in% c("CA2011", "CA2020") ~ "Adult",
                           CountStage %in% c("CT2011", "CT2020") ~ "Total"),
         Label = case_when(Stage %in% "Juvenile" ~ "a",
                           Stage %in% "Subadult" ~ "b",
                           Stage %in% "Adult" ~ "c",
                           Stage %in% "Total" ~ "d"),
         Stage = factor(Stage, levels = c("Juvenile", "Subadult", "Adult", "Total")),
         p_value = case_when(CountStage %in% c("CJ2011", "CJ2020") ~ 
                               pop.diff.cj$p.value,
                             CountStage %in% c("CS2011", "CS2020") ~ 
                               pop.diff.cs$p.value,
                             CountStage %in% c("CA2011", "CA2020") ~ 
                               pop.diff.ca$p.value,
                             CountStage %in% c("CT2011", "CT2020") ~ 
                               pop.diff.ct$p.value)) %>%
  group_by(Stage) %>%
  mutate(label.y = max(Count)) %>% ungroup() %>%
  ggpaired(x = "Year", y = "Count", id = "Plot", 
           color = "Year", line.color = alpha("grey", 0.2),
           line.size = 0.4, palette = "jco") +
  # wilcox paired test
  stat_compare_means(paired = TRUE, label.x = 1.2, size = 3) +
  geom_text(aes(x = 0.5,  y = label.y, label = Label, size = 4)) +
  facet_wrap(~Stage, nrow = 2, scales = "free") + 
  theme_classic() + mythemes +
  labs(x = "Year", y = "Cactus per plot") +
  theme(legend.position = "none") -> cactus.wilcox.plot

cactus.wilcox.plot

At all stages, we see changes in cactus density. There is a very weak change in adult cactus.

Let’s just tabulate a summary of cactus density in our plots before and after tortoise reintroduction.

t(
    sapply(iguana_plots[,16:23], function(...) 
      list(means = mean(..., na.rm = T)/((pi*25^2)/10000), 
           se = (sd(..., na.rm = T)/sqrt(43))/((pi*25^2)/10000)))
  )

##        means    se      
## CA2011 56.85163 6.152795
## CS2011 9.830594 1.65535 
## CJ2011 12.19941 1.940855
## CT2011 78.88163 7.432893
## CA2020 45.71818 4.382008
## CS2020 24.39882 3.345125
## CJ2020 36.00603 4.936571
## CT2020 106.123  7.770257

Iguana count GLMM

We’ll mixed models to compare iguana plot counts of iguanas and cactus in 2011 and 2020 with the lme4 package. This will help us understand the direction of these trends for cactus.

Let’s connect our tortoise density raster to the iguana plot data. I’ll create a shapefile from the plot points, and summarize the recent (5yr average) tortoise density surrounding those points (50m buffer).

# create shapefile for plots
iguana_plots_shp <- iguana_plots
coordinates(object = iguana_plots_shp) <- ~ Lon + Lat
proj4string(iguana_plots_shp) <- CRS("+proj=longlat +datum=WGS84")
iguana_plots_shp <- spTransform(iguana_plots_shp, 
                                CRSobj = CRS("+init=epsg:32715"))

# create buffer for plots
library(rgeos)
plot_buffers <- gBuffer(iguana_plots_shp, byid = TRUE, width = 50, 
                        capStyle="ROUND")

# get zonal statistics for tortoise densities in iguana plot buffers
iguana_plots$tden <- c(raster::extract(tortoise.brick.adj[[6]], 
                                       plot_buffers,
                                       fun = mean, na.rm = TRUE))
iguana_plots$tden5y <- c(raster::extract(mean(tortoise.brick.adj[[1:5]]), 
                                         plot_buffers,
                                         fun = mean, na.rm = TRUE))

# divide tortoise density values into "high" and "low" density treatments
iguana_plots$tdencat <- 
  as.factor(ifelse(iguana_plots$tden5y < quantile(iguana_plots$tden5y, 0.5), 
                   "low", "high"))

library(reshape2)
# melt iguana data
iguana.melt <- iguana_plots %>%
  dplyr::select(c(Plot, ITM2011, ITM2020, ITH2011, ITH2020, 
                  ITJ2011, ITJ2020, ITT2011, ITT2020, tden5y, tdencat)) %>%
  melt(id = c("Plot", "tden5y", "tdencat"))

# melt cactus data
cactus.melt.juv <- iguana_plots %>%
  dplyr::select(c(Plot, CJ2011, CJ2020)) %>%
  melt(id = c("Plot")) %>%
  mutate(CJ = value,
         year = as.factor(ifelse(variable %in% "CJ2011", "2011", "2020"))) %>%
  dplyr::select(c(Plot, year, CJ))

cactus.melt.sub <- iguana_plots %>%
  dplyr::select(c(Plot, CS2011, CS2020)) %>%
  melt(id = c("Plot")) %>%
  mutate(CS = value,
         year = as.factor(ifelse(variable %in% "CS2011", "2011", "2020"))) %>%
  dplyr::select(c(Plot, year, CS))

cactus.melt.adu <- iguana_plots %>%
  dplyr::select(c(Plot, CA2011, CA2020)) %>%
  melt(id = c("Plot")) %>%
  mutate(CA = value,
         year = as.factor(ifelse(variable %in% "CA2011", "2011", "2020"))) %>%
  dplyr::select(c(Plot, year, CA))

cactus.melt.tot <- iguana_plots %>%
  dplyr::select(c(Plot, CT2011, CT2020)) %>%
  melt(id = c("Plot")) %>%
  mutate(CT = value,
         year = as.factor(ifelse(variable %in% "CT2011", "2011", "2020"))) %>%
  dplyr::select(c(Plot, year, CT))

# create data frame of iguana and cactus plot counts for GLMMs
iguana.total <- iguana.melt %>%
  filter(variable %in% "ITT2011" | variable %in% "ITT2020") %>%
  mutate(year = as.factor(ifelse(variable %in% "ITT2011", "2011", "2020"))) %>%
  left_join(cactus.melt.juv, by = c("Plot", "year")) %>%
  left_join(cactus.melt.sub, by = c("Plot", "year")) %>%
  left_join(cactus.melt.adu, by = c("Plot", "year")) %>%
  left_join(cactus.melt.tot, by = c("Plot", "year")) %>%
  mutate(status = as.factor(ifelse(value > 0, 1, 0)),
         iguanas = value)

Now let’s build our GLMM and plot out the time * tortoise contrast.

library(lme4)
library(lmerTest)
library(DHARMa)
library(ggeffects)

iguana.total$tdencat <- factor(iguana.total$tdencat, levels = c("low", "high"))

# models
## null
iguana.null <-glmer(iguanas ~ 1 + (1|Plot), 
                  family = poisson, data = iguana.total)
## time
iguana.year <-glmer(iguanas ~ year + (1|Plot), 
                  family = poisson, data = iguana.total)
## tortoise
iguana.yearXtort <- glmer(iguanas ~ year * tdencat + (1|Plot), 
                    family = poisson, data = iguana.total)

# compare null to fitted models with Likelihood ratio test
library(lmtest)
lrtest(iguana.null, iguana.year, iguana.yearXtort)

## Likelihood ratio test
## 
## Model 1: iguanas ~ 1 + (1 | Plot)
## Model 2: iguanas ~ year + (1 | Plot)
## Model 3: iguanas ~ year * tdencat + (1 | Plot)
##   #Df  LogLik Df  Chisq Pr(>Chisq)  
## 1   2 -83.615                       
## 2   3 -83.068  1 1.0933    0.29574  
## 3   5 -78.957  2 8.2223    0.01639 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# inspect model residuals
simulationOutput <- simulateResiduals(fittedModel = iguana.yearXtort)
plot(simulationOutput)

summary(iguana.yearXtort) 

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: iguanas ~ year * tdencat + (1 | Plot)
##    Data: iguana.total
## 
##      AIC      BIC   logLik deviance df.resid 
##    167.9    180.2    -79.0    157.9       81 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -0.8855 -0.6031 -0.4302  0.7720  3.1303 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  Plot   (Intercept) 0.2714   0.521   
## Number of obs: 86, groups:  Plot, 43
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)   
## (Intercept)           -1.5664     0.4802  -3.262  0.00111 **
## year2020               0.3365     0.5855   0.575  0.56556   
## tdencathigh            1.3862     0.5252   2.639  0.00831 **
## year2020:tdencathigh  -0.8961     0.6883  -1.302  0.19299   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) yr2020 tdncth
## year2020    -0.711              
## tdencathigh -0.853  0.650       
## yr2020:tdnc  0.605 -0.851 -0.685

# get predictions from fitted model
## iguana count predictions over tortoise and time contrast
ggpredict(iguana.yearXtort, terms = c("year", "tdencat"), 
          type = "fe", ci.lvl = 0.95)  %>%
  mutate(predicted = predicted / ((pi*25^2)/100^2),
         conf.low = conf.low / ((pi*25^2)/100^2),
         conf.high = conf.high / ((pi*25^2)/100^2)) -> iguana.pred

# plot iguana density predictions
quadrant.plot <-
  ggplot(iguana.pred, aes(x = x, y = predicted, group = group, fill = group)) +
  geom_col(stat = "identity", position = position_dodge(0.5), width = 0.4) + 
  geom_errorbar(aes(ymin = conf.low, ymax = conf.high), 
                position = position_dodge(0.5), width = 0) +
  scale_fill_manual(values = c("grey50", "grey15"), name = "Tortoise density") +
  theme_classic() + mythemes + labs(x = "Year", y = "Iguana density (per ha)") +
  theme(legend.position = c(.8,.8), legend.title = element_text(size = 13), 
        legend.text = element_text(size = 12))

quadrant.plot

This model from the plot data tells that the total iguana population has not changed much from 2011 to present. Overall, the plots suggest a slight decline in the tortoise release zone after repatriation (in contrast to the distance sampling data). The distribution of iguanas may have shifted, with tortoises displacing some iguanas to other areas that were less occupied before. But the interaction between tortoise density and time was very weak.

Cactus count GLMMs

Let’s finally look at how cactus densities have changed over time with tortoises using the same model structure. Starting with juvenile cactus.

# models
## null
cactus.null <-glmer(CJ ~ 1 + (1|Plot), 
                  family = poisson, data = iguana.total)
## time
cactus.year <-glmer(CJ ~ year + (1|Plot), 
                  family = poisson, data = iguana.total)
## time x tortoise
cactus.yearXtort <- glmer(CJ ~ year * tdencat + (1|Plot), 
                    family = poisson, data = iguana.total)

# compare null to fitted with Likelihood ratio test
lrtest(cactus.null, cactus.year, cactus.yearXtort)

## Likelihood ratio test
## 
## Model 1: CJ ~ 1 + (1 | Plot)
## Model 2: CJ ~ year + (1 | Plot)
## Model 3: CJ ~ year * tdencat + (1 | Plot)
##   #Df  LogLik Df    Chisq Pr(>Chisq)    
## 1   2 -262.34                           
## 2   3 -210.46  1 103.7549    < 2e-16 ***
## 3   5 -207.36  2   6.2053    0.04493 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# inspect model residuals
simulationOutput <- simulateResiduals(fittedModel = cactus.yearXtort)
plot(simulationOutput)

summary(cactus.yearXtort) 

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: CJ ~ year * tdencat + (1 | Plot)
##    Data: iguana.total
## 
##      AIC      BIC   logLik deviance df.resid 
##    424.7    437.0   -207.4    414.7       81 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.6150 -0.7514 -0.1252  0.3131  3.0284 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  Plot   (Intercept) 0.3343   0.5782  
## Number of obs: 86, groups:  Plot, 43
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)            0.3002     0.2136   1.405   0.1600    
## year2020               1.3573     0.1868   7.266 3.71e-13 ***
## tdencathigh            0.6766     0.2749   2.461   0.0138 *  
## year2020:tdencathigh  -0.4528     0.2346  -1.931   0.0535 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) yr2020 tdncth
## year2020    -0.696              
## tdencathigh -0.770  0.540       
## yr2020:tdnc  0.554 -0.796 -0.653

# get predictions from fitted model
## iguana count predictions over tortoise and time contrast
ggpredict(cactus.yearXtort, terms = c("year", "tdencat"), 
          type = "fe", ci.lvl = 0.95)  %>%
  mutate(predicted = predicted / ((pi*25^2)/100^2),
         conf.low = conf.low / ((pi*25^2)/100^2),
         conf.high = conf.high / ((pi*25^2)/100^2)) -> cactus.pred


cactus.pred <- ggpredict(cactus.yearXtort, terms = c("year", "tdencat"), 
                         type = "fe", ci.lvl = 0.95) %>%
  mutate(predicted = predicted / ((pi*25^2)/100^2),
         conf.low = conf.low / ((pi*25^2)/100^2),
         conf.high = conf.high / ((pi*25^2)/100^2))

# plot iguana density predictions
quadrant.cj.plot <-
  ggplot(cactus.pred, aes(x = x, y = predicted, group = group, fill = group)) +
  geom_col(stat = "identity", position = position_dodge(0.5), width = 0.4) + 
  geom_errorbar(aes(ymin = conf.low, ymax = conf.high), 
                position = position_dodge(0.5), width = 0) +
  scale_fill_manual(values = c("grey50", "grey15"), name = "Tortoise density") +
  theme_classic() + mythemes +
  labs(x = "Year", y = expression(Juveniles ~ ha^-1)) +
  theme(legend.position = "top", legend.title = element_text(size = 13), 
        legend.text = element_text(size = 12))

quadrant.cj.plot

Juvenile cactus counts have increased—almost tripled—before and after tortoise introduction. There is also a positive effect of tortoise density on juvenile cactus. Worth noticing that the high density tortoise areas seemed to have more cactus before there were any tortoise, which may just reflect the similar habitat selection strategies of iguanas at these different sites.

What about subadult cactus?

# models
## null
cactus.null <-glmer(CS ~ 1 + (1|Plot), 
                  family = poisson, data = iguana.total)
## time
cactus.year <-glmer(CS ~ year + (1|Plot), 
                  family = poisson, data = iguana.total)
## time x tortoise
cactus.yearXtort <- glmer(CS ~ year * tdencat + (1|Plot), 
                    family = poisson, data = iguana.total)

# compare null to fitted with Likelihood ratio test
lrtest(cactus.null, cactus.year, cactus.yearXtort)

## Likelihood ratio test
## 
## Model 1: CS ~ 1 + (1 | Plot)
## Model 2: CS ~ year + (1 | Plot)
## Model 3: CS ~ year * tdencat + (1 | Plot)
##   #Df  LogLik Df   Chisq Pr(>Chisq)    
## 1   2 -218.93                          
## 2   3 -191.90  1 54.0570  1.948e-13 ***
## 3   5 -188.43  2  6.9392    0.03113 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# inspect model residuals
simulationOutput <- simulateResiduals(fittedModel = cactus.yearXtort)
plot(simulationOutput)

summary(cactus.yearXtort) 

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: CS ~ year * tdencat + (1 | Plot)
##    Data: iguana.total
## 
##      AIC      BIC   logLik deviance df.resid 
##    386.9    399.1   -188.4    376.9       81 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.54624 -0.87081 -0.05151  0.48314  2.42293 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  Plot   (Intercept) 0.3443   0.5867  
## Number of obs: 86, groups:  Plot, 43
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)            0.2369     0.2237   1.059 0.289669    
## year2020               0.7577     0.2170   3.491 0.000482 ***
## tdencathigh            0.4353     0.2917   1.492 0.135670    
## year2020:tdencathigh   0.2279     0.2689   0.848 0.396715    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) yr2020 tdncth
## year2020    -0.661              
## tdencathigh -0.754  0.507       
## yr2020:tdnc  0.533 -0.807 -0.643

# get predictions from fitted model
## iguana count predictions over tortoise and time contrast
cactus.pred <- ggpredict(cactus.yearXtort, terms = c("year", "tdencat"), 
                         type = "fe", ci.lvl = 0.95)%>%
  mutate(predicted = predicted / ((pi*25^2)/100^2),
         conf.low = conf.low / ((pi*25^2)/100^2),
         conf.high = conf.high / ((pi*25^2)/100^2)) 

# plot iguana density predictions
quadrant.cs.plot <-
  ggplot(cactus.pred, aes(x = x, y = predicted, group = group, fill = group)) +
  geom_col(stat = "identity", position = position_dodge(0.5), width = 0.4) + 
  geom_errorbar(aes(ymin = conf.low, ymax = conf.high), 
                position = position_dodge(0.5), width = 0) +
  scale_fill_manual(values = c("grey50", "grey15"), name = "Tortoise density") +
  theme_classic() + mythemes + 
  labs(x = "Year", y = expression(Subadults ~ ha^-1)) +
  theme(legend.position = "top", legend.title = element_text(size = 13), 
        legend.text = element_text(size = 12))

quadrant.cs.plot

Again we see an increase in subadult cactus. The effect here is weaker than for juveniles. No effect of tortoise density here.

What about adult cactus? We shouldn’t see a noticeable change here.

# models
## null
cactus.null <-glmer(CA ~ 1 + (1|Plot), 
                  family = poisson, data = iguana.total)
## time
cactus.year <-glmer(CA ~ year + (1|Plot), 
                  family = poisson, data = iguana.total)
## time x tortoise
cactus.yearXtort <- glmer(CA ~ year * tdencat + (1|Plot), 
                    family = poisson, data = iguana.total)

# compare null to fitted with Likelihood ratio test
lrtest(cactus.null, cactus.year, cactus.yearXtort)

## Likelihood ratio test
## 
## Model 1: CA ~ 1 + (1 | Plot)
## Model 2: CA ~ year + (1 | Plot)
## Model 3: CA ~ year * tdencat + (1 | Plot)
##   #Df  LogLik Df   Chisq Pr(>Chisq)   
## 1   2 -271.67                         
## 2   3 -266.56  1 10.2234   0.001387 **
## 3   5 -266.26  2  0.5873   0.745536   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# inspect model residuals
simulationOutput <- simulateResiduals(fittedModel = cactus.yearXtort)
plot(simulationOutput)

summary(cactus.yearXtort) 

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: CA ~ year * tdencat + (1 | Plot)
##    Data: iguana.total
## 
##      AIC      BIC   logLik deviance df.resid 
##    542.5    554.8   -266.3    532.5       81 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -1.83013 -0.69705 -0.05213  0.56000  2.02722 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  Plot   (Intercept) 0.4205   0.6485  
## Number of obs: 86, groups:  Plot, 43
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)           2.30790    0.15830  14.579   <2e-16 ***
## year2020             -0.22884    0.09170  -2.496   0.0126 *  
## tdencathigh          -0.17118    0.22149  -0.773   0.4396    
## year2020:tdencathigh  0.02405    0.13605   0.177   0.8597    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) yr2020 tdncth
## year2020    -0.257              
## tdencathigh -0.709  0.183       
## yr2020:tdnc  0.173 -0.674 -0.274

# get predictions from fitted model
## iguana count predictions over tortoise and time contrast
cactus.pred <- ggpredict(cactus.yearXtort, terms = c("year", "tdencat"), 
                         type = "fe", ci.lvl = 0.95) %>%
  mutate(predicted = predicted / ((pi*25^2)/100^2),
         conf.low = conf.low / ((pi*25^2)/100^2),
         conf.high = conf.high / ((pi*25^2)/100^2))

# plot iguana density predictions
quadrant.ca.plot <-
  ggplot(cactus.pred, aes(x = x, y = predicted, group = group, fill = group)) +
  geom_col(stat = "identity", position = position_dodge(0.5), width = 0.4) + 
  geom_errorbar(aes(ymin = conf.low, ymax = conf.high), 
                position = position_dodge(0.5), width = 0) +
  scale_fill_manual(values = c("grey50", "grey15"), name = "Tortoise density") +
  theme_classic() + mythemes + 
  labs(x = "Year", y = expression(Adults ~ ha^-1)) +
  theme(legend.position = "top", legend.title = element_text(size = 13), 
        legend.text = element_text(size = 12))

quadrant.ca.plot

There is a slight decline in adult cactus counts from 2011 to 2020.

Let’s look at total cactus change.

# models
## null
cactus.null <-glmer(CT ~ 1 + (1|Plot), 
                  family = poisson, data = iguana.total)
## year
cactus.year <- glmer(CT ~ year + (1|Plot), 
                    family = poisson, data = iguana.total)
## fitted
cactus.yearXtort <- glmer(CT ~ year * tdencat + (1|Plot), 
                    family = poisson, data = iguana.total)

# compare null to fitted with Likelihood ratio test
lrtest(cactus.null, cactus.year, cactus.yearXtort)

## Likelihood ratio test
## 
## Model 1: CT ~ 1 + (1 | Plot)
## Model 2: CT ~ year + (1 | Plot)
## Model 3: CT ~ year * tdencat + (1 | Plot)
##   #Df  LogLik Df   Chisq Pr(>Chisq)    
## 1   2 -337.61                          
## 2   3 -320.61  1 33.9903  5.539e-09 ***
## 3   5 -319.56  2  2.0975     0.3504    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# inspect model residuals
simulationOutput <- simulateResiduals(fittedModel = cactus.yearXtort)
plot(simulationOutput)

summary(cactus.yearXtort) 

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: poisson  ( log )
## Formula: CT ~ year * tdencat + (1 | Plot)
##    Data: iguana.total
## 
##      AIC      BIC   logLik deviance df.resid 
##    649.1    661.4   -319.6    639.1       81 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5096 -0.8189 -0.0740  0.6368  3.5074 
## 
## Random effects:
##  Groups Name        Variance Std.Dev.
##  Plot   (Intercept) 0.2443   0.4942  
## Number of obs: 86, groups:  Plot, 43
## 
## Fixed effects:
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)           2.65127    0.12219  21.698  < 2e-16 ***
## year2020              0.22010    0.07361   2.990  0.00279 ** 
## tdencathigh          -0.04210    0.17088  -0.246  0.80538    
## year2020:tdencathigh  0.14603    0.10194   1.432  0.15201    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) yr2020 tdncth
## year2020    -0.334              
## tdencathigh -0.712  0.239       
## yr2020:tdnc  0.241 -0.722 -0.341

# get predictions from fitted model
## iguana count predictions over tortoise and time contrast
cactus.pred <- ggpredict(cactus.yearXtort, terms = c("year", "tdencat"), 
                         type = "fe", ci.lvl = 0.95) %>%
  mutate(predicted = predicted / ((pi*25^2)/100^2),
         conf.low = conf.low / ((pi*25^2)/100^2),
         conf.high = conf.high / ((pi*25^2)/100^2))

# plot iguana density predictions
quadrant.ct.plot <-
  ggplot(cactus.pred, aes(x = x, y = predicted, group = group, fill = group)) +
  geom_col(stat = "identity", position = position_dodge(0.5), width = 0.4) + 
  geom_errorbar(aes(ymin = conf.low, ymax = conf.high), 
                position = position_dodge(0.5), width = 0) +
  scale_fill_manual(values = c("grey50", "grey15"), 
                    name = "Tortoise density") +
  theme_classic() + mythemes + labs(x = "Year", y = expression(Total ~ ha^-1)) +
  theme(legend.position = "top", legend.title = element_text(size = 13), 
        legend.text = element_text(size = 12))

quadrant.ct.plot

Overall, we see an increase in cactus in the tortoise release zone on Santa Fe between 2011 and 2020. The overall change is independent of tortoise density variation, but as we saw before that variable is informative for certain cactus stages.

Let’s pull all these cactus figures together.

ggarrange(quadrant.cj.plot, quadrant.cs.plot, 
          quadrant.ca.plot, quadrant.ct.plot,
          nrow = 2, ncol = 2, labels = c("a", "b", "c", "d"), align = "hv",
          label.x = c(0.19, 0.19, 0.19, 0.19), common.legend = TRUE)

It may also be helpful to visualize changes in proportions of different age classes of cactus from 2011 to 2020.

iguana.class.tab <-
  data.frame(year = rep(iguana.total$year, 3),
             iguana = c(iguana.total$CJ, iguana.total$CS, iguana.total$CA),
             type = c(rep("Juvenile", nrow(iguana.total)), 
                      rep("Subadult", nrow(iguana.total)),
                      rep("Adult", nrow(iguana.total))),
             total = rep(iguana.total$CT, 3))

iguana.class.tab %>%
  mutate(prop = iguana / total,
         type = factor(type, levels = c("Adult", "Subadult", "Juvenile"))) %>%
  group_by(type, year) %>%
  summarise(mean_prop = mean(prop),
            se_prop = sd(prop)/sqrt(n())) %>%
  ungroup() -> iguana.class.props 

cactus.prop.plot <-
  ggplot(iguana.class.props, aes(x = year, fill = type)) +
  geom_bar(aes(y = mean_prop), stat = "identity") +
  geom_text(aes(label = round(mean_prop,2), y = mean_prop), 
            position = position_stack(vjust = 0.5), size = 4) +
  scale_fill_manual(values = col2[c(2:4)], name = "Stage") +
  labs(x = "Year", y = "Proportion of cactus") + 
  theme_classic() + mythemes 

cactus.prop.plot

Future monitoring, especially a repeat of the full-island iguana survey, will be essential for describing iguana and cactus demographic change with the growing tortoise population.

   

Session info

---

sessionInfo()

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18362)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252 
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] grid      stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] lmtest_0.9-37       zoo_1.8-8           ggeffects_0.15.1   
##  [4] DHARMa_0.3.2.0      lmerTest_3.1-2      lme4_1.1-23        
##  [7] Matrix_1.2-18       rgeos_0.5-3         broom_0.7.0        
## [10] adehabitatHR_0.4.18 adehabitatLT_0.3.25 CircStats_0.2-6    
## [13] boot_1.3-25         MASS_7.3-51.6       adehabitatMA_0.3.14
## [16] ade4_1.7-15         deldir_0.1-28       colorRamps_2.3     
## [19] gridExtra_2.3       viridis_0.5.1       viridisLite_0.3.0  
## [22] AICcmodavg_2.3-0    unmarked_1.0.1      ggridges_0.5.2     
## [25] rasterVis_0.48      latticeExtra_0.6-29 lattice_0.20-41    
## [28] spatstat_1.64-1     rpart_4.1-15        spatstat.data_1.4-3
## [31] ggsn_0.5.0          maptools_1.0-1      sf_0.9-5           
## [34] rgdal_1.5-15        raster_3.3-13       sp_1.4-2           
## [37] popbio_2.7          cowplot_1.0.0       kableExtra_1.1.0   
## [40] reshape2_1.4.4      ggpubr_0.4.0        tidymv_3.0.0       
## [43] readxl_1.3.1        forcats_0.5.0       stringr_1.4.0      
## [46] dplyr_1.0.1         purrr_0.3.4         readr_1.3.1        
## [49] tidyr_1.1.1         tibble_3.0.3        tidyverse_1.3.0    
## [52] lubridate_1.7.9     lisa_0.1.1          ggExtra_0.9        
## [55] ggthemes_4.2.0      mgcv_1.8-31         nlme_3.1-148       
## [58] ggalt_0.4.0         ggplot2_3.3.2       RMark_2.2.7        
## [61] knitr_1.29         
## 
## loaded via a namespace (and not attached):
##   [1] utf8_1.1.4            tidyselect_1.1.0      htmlwidgets_1.5.1    
##   [4] munsell_0.5.0         codetools_0.2-16      units_0.6-7          
##   [7] statmod_1.4.34        miniUI_0.1.1.1        withr_2.2.0          
##  [10] colorspace_1.4-1      highr_0.8             rstudioapi_0.11      
##  [13] stats4_4.0.2          ggsignif_0.6.0        tensor_1.5           
##  [16] Rttf2pt1_1.3.8        labeling_0.3          RgoogleMaps_1.4.5.3  
##  [19] polyclip_1.10-0       farver_2.0.3          coda_0.19-3          
##  [22] vctrs_0.3.2           generics_0.0.2        xfun_0.16            
##  [25] R6_2.4.1              VGAM_1.1-3            bitops_1.0-6         
##  [28] spatstat.utils_1.17-0 assertthat_0.2.1      promises_1.1.1       
##  [31] scales_1.1.1          nnet_7.3-14           gtable_0.3.0         
##  [34] ash_1.0-15            goftest_1.2-2         rlang_0.4.7          
##  [37] splines_4.0.2         rstatix_0.6.0         extrafontdb_1.0      
##  [40] acepack_1.4.1         hexbin_1.28.1         checkmate_2.0.0      
##  [43] yaml_2.2.1            abind_1.4-5           modelr_0.1.8         
##  [46] backports_1.1.8       httpuv_1.5.4          Hmisc_4.4-0          
##  [49] extrafont_0.17        tools_4.0.2           ellipsis_0.3.1       
##  [52] RColorBrewer_1.1-2    Rcpp_1.0.5            plyr_1.8.6           
##  [55] base64enc_0.1-3       classInt_0.4-3        ggmap_3.0.0          
##  [58] haven_2.3.1           cluster_2.1.0         fs_1.5.0             
##  [61] magrittr_1.5          data.table_1.13.0     openxlsx_4.1.5       
##  [64] reprex_0.3.0          mvtnorm_1.1-1         matrixcalc_1.0-3     
##  [67] hms_0.5.3             mime_0.9              evaluate_0.14        
##  [70] xtable_1.8-4          rio_0.5.16            jpeg_0.1-8.1         
##  [73] compiler_4.0.2        maps_3.3.0            KernSmooth_2.23-17   
##  [76] crayon_1.3.4          minqa_1.2.4           htmltools_0.5.0      
##  [79] later_1.1.0.1         Formula_1.2-3         expm_0.999-5         
##  [82] DBI_1.1.0             sjlabelled_1.1.6      dbplyr_1.4.4         
##  [85] proj4_1.0-10          car_3.0-8             cli_2.0.2            
##  [88] insight_0.9.0         parallel_4.0.2        pkgconfig_2.0.3      
##  [91] numDeriv_2016.8-1.1   foreign_0.8-80        foreach_1.5.0        
##  [94] xml2_1.3.2            webshot_0.5.2         rvest_0.3.6          
##  [97] snakecase_0.11.0      digest_0.6.25         msm_1.6.8            
## [100] rmarkdown_2.3         cellranger_1.1.0      htmlTable_2.0.1      
## [103] gap_1.2.2             curl_4.3              shiny_1.5.0          
## [106] nloptr_1.2.2.2        rjson_0.2.20          lifecycle_0.2.0      
## [109] jsonlite_1.7.0        carData_3.0-4         fansi_0.4.1          
## [112] pillar_1.4.6          ggsci_2.9             fastmap_1.0.1        
## [115] httr_1.4.2            survival_3.1-12       glue_1.4.1           
## [118] zip_2.0.4             iterators_1.0.12      png_0.1-7            
## [121] class_7.3-17          stringi_1.4.6         blob_1.2.1           
## [124] e1071_1.7-3